Yeah, this is one of those situations where there's theory and practice. Each individual step in the development of Union corps is logical but by the end of the process they are functionally reinforced divisions on average.
The process of development in the East is:
March 1862: the Army of the Potomac has a large number of divisions, which are occasionally task-organized into multi-division units over the winter.
March 1862: Per orders from Lincoln, the AoP is divided into five corps. These five corps distribute what amounts to 14 divisions between them; these are proper corps because each one (aside from 5th) contains three full-strength divisions. Then when Blenker is detached this leaves the corps numbering 3,2,3,3,2 divisions; all of them are corps-scale, and each of their divisions averages about 14 regiments.
April 1862: 1st and 5th Corps removed from the AoP, but Franklin's division returned. The AoP corps structure in divisions is now 2,3,3 with an independent division (Franklin's.)
May 1862: after Williamsburg, permission granted to temporarily reorganize the corps. To equalize them, McClellan elevates Sykes' regular infantry brigade to a division by adding the provost guard and other army-level units; this permits the creation of a five-corps structure 2,2,2,2,2 divisions, though Porter's 5th Corps is the weakest because that's the one that got Sykes' new and understrength division.
June 1862: with the addition of McCall's division, Porter's 5th Corps is now the strongest, though the Peninsular campaign inflicts serious casualties on the AoP; between straggling and so on, the 11 divisions making it up have dropped from about 10,500 men on average to about 8,000 men on average.
Note that this means that a triangular corps would have been 24,000 men (PFD) instead of 31,000 men PFD. Because they're binary, though, the average corps is about 16,000 men (with Porter's 5th Corps being stronger due to its extra division, though not 50% stronger).
In July, Pope combines two departments (Shenandoah and Rappahannock) along with the field force of a third (Mountains) to form his own Army of Virginia. These each becomes a corps of the Army of Virginia, but they're very lopsided - the Dept. Rappahannock was wildly larger than the other two forces and is twice the size of the other two corps, but to equalize them would mean taking lots of troops from McDowell and that was either untenable or didn't occur to anyone.
Note for example that Sigel's corps consists of 22 infantry regiments and 14 of them are from Blenker's division; Banks' corps consists of 23 infantry regiments. McDowell's corps has two divisions, both of which are 16 regiments.
9th Corps meanwhile is a reinforcement force (originally for McClellan, then diverted) which is made up of three small binary divisions. In total size it is somewhat larger than an "original" AoP division, but much less than two. Despite having three divisions it only has 19 regiments.
During the fighting in Second Bull Run I have found it easiest to consider 5th Corps, Banks' Corps, 9th Corps and Sigel's Corps to be overstrength divisions, and that Heintzelman has two divisions and McDowell has three (the third being the Pennsylvania Reserves). It's not a perfect model but it better expresses the size disparity in the corps as a result of their varying histories and regiment counts.
After casualties in Second Bull Run, these disparate corps are combined into a single organization, and the accession of reinforcement regiments expands them somewhat, but because it's not viable or not "the done thing" to dissolve a formal corps the result is that the army that McClellan takes out (which numbers around 90,000 men as it marches out of Washington, before the addition of Morell and Humphreys) consists of elements of at least seven corps; at that, that's with the reinforcements and before the addition of reinforcements it would have been less than 80,000.
Some of this is just casualties. 1st Corps consists of three "full strength" original divisions and so should be 30,000 men or so before new regiments; 2nd Corps should be 20,000 men or so before reinforcements; 6th Corps should also be 20,000 men or so, and 5th Corps should be something like 16,000. Those four corps, without the impact of months of casualties and straggling, should amount to more men than McClellan actually has veterans in his entire army. Then Couch is half of 4th Corps (and so "should" be another 10,000 or so). All of these formations, if full strength, should be "corps size".
But other parts of it are due to formally named corps which were the size they were because they were either created small or had large force transfers out of them. This is 9th Corps (which as created is barely larger than a "full size" division) and Banks' corps (which had started life as the Department of the Shenandoah at 31 regiments, a creditable size for a binary corps, but lost 21 of them to the Dept. of the Rappahannock and only ever got 12 back)
The reason why the 6th Corps is so big comes about as a result of Antietam and afterwards. 6th Corps first isn't heavily engaged at Antietam (so it doesn't suffer further casualties knocking its size down, having already avoided the fighting at Second bull Run; 2nd Corps missed Second Bull Run but then suffered very heavily at Antietam) and then it absorbs Couch's division which had also avoided both sanguinary battles. This makes 6th Corps a "proper" corps, with its replacements in "green" regiments having nearly kept up with casualties and attrition simply because it's not suffered much in heavy battles; all the other AoP corps either started small or have been beaten about heavily enough that they're small now. Consequently they're somewhere closer to half of the "proper" corps size.
3rd Corps is also quite big because it's stuffed with replacements over this period and misses Antietam. As a result it has two very large full-strength divisions and also a third weaker division at the end of Loudoun Valley.
Of course, after that the fighting at Fredericksburg continues the attrition process.
The Confederate trajectory is completely different. At the Seven Days they were still using "divisions" as their highest level of command, though these were often six-brigade divisions that were operated as two "demi-divisions" and so were the same size as Union corps but did not have that title; importantly, when Lee heads north for Northern Virginia and Maryland he is still using an ad-hoc structure at the highest levels. Longstreet's Command and Jackson's command represent real organizations but not formal organizations, and so does DH Hill's reinforcement command; consequently Lee is perfectly at liberty to break up DH Hill's command into its component parts. During Maryland, in fact, Lee effectively operates on an ad-hoc four-corps structure (Jackson, Longstreet, McLaws, DH Hill) with Walker as an independent division; all four of the bracketed formations would not look out of place as Union corps in terms of organizational and numerical strength.
Then after Maryland when Lee actually does formalize his corps structure, for personal reasons (i.e. he does not want to give DH Hill a formal corps command, and DH Hill is third in seniority among his subordinates) he adopts a two-corps structure. The result of this is that Lee's army splits its strength over just two corps at a time when the Army of the Potomac consists of six (1st 2nd 5th 6th 9th 12th), and Lee's corps are much closer to "proper corps" size - very close actually, nearly the same as the AoP corps from March. But in October, take 6th out of the picture and the other five AoP corps are roughly half the size of Lee's corps on average.
This is purely organizational. Lee could very easily have picked a three-corps structure, in which case his corps would be about the size of AoP corps from May 1862 when they were binary; by the time Lee actually does go three-corps he's gained somewhat in strength compared to November 1862, and so his three corps are each a bit bigger than that. Because most of the AoP corps have suffered from expiring enlistments and further attrition, in Gettysburg it's again the case that 6th is the outlier, but once more the other Union corps are much weaker on average than Lee's corps.
It's not until the winter of 1863-4 that the Union corps of the AoP specifically consolidate again.
There are several reasons to have a corps structure, and the most important is probably to break up the top level commander's assets into a manageable number of components, each of which can be somewhere and given a task - it is a way to manage the complexity of operations. The Union rigidity in being unable to dissolve corps to keep the others up to a consistent notional strength probably does make the job of the high level commander more difficult, though not unmanageably so; the way that wings/grand divisions keep emerging to combine multiple weak corps into a single manoeuvre element the size of a "proper corps" shows the utility of the size.
At some point the Union seems to have decided that the corps should be a top-level organizational element for the entire army (thus why an entire army gets designated as a corps) which probably interferes with actually running the army. It probably would have been superior from an organizational level to either leave corps structure entirely up to the field commander, or to formalize the "grand division" concept, or for Lincoln to be willing to take corps out of circulation if they were clearly too small (earlier than this actually happened, that is).
As a separate point I'd argue that the faff about getting cavalry to the Peninsula (for the Union), sheer scarcity of cavalry, and the over-reliance on the idea of massed cavalry for raiding all probably impeded the concept of the corps as a true combined-arms formation. A doctrinal corps should have infantry, artillery and cavalry but that last point is lacking on the org chart - probably mostly because there simply is not enough to go around early on and by Chancellorsville (if not sooner) the pattern of having the cavalry as an independent organization able to do things independently had become set to the detriment of both sides (to different degrees).