So the basic issue with an overland movement is that the Confederates can refuse battle (by retiring) unless you can either cut them off from Richmond (forcing them to break out) or threaten Richmond itself. Consequently, each line of defence that you have to overcome is an avenue for them to present you with a battle they want to take.
Going directly down the Orange and Alexandria, this means fighting for Manassass/Centreville and the line of the Bull Run, then the line of the Broad Run (potentially), then the line of the Cedar Run, then the line of the Rappahannock. Once all four of those lines have been overcome, you're where Grant's Overland started - and that one required Lee to be out of position and more than twice Lee's total numbers, while Johnston (when he defended the line of the Rapidan) was not out of position in the way that Lee was.
In addition, Grant's Overland logistically required the York river to be open for Union supplies - that's how Grant got around Lee's blocking positions that Grant could not overcome frontally. But without the Peninsular campaign, the York isn't open; the North Anna position is a blocker that can't be overcome by manoeuvre.
Johnston here is suggesting specifically that McClellan's army would march south to near Fredericksburg, but that it would do so in Maryland, and then cross the Potomac by shipping before moving to cross the Rappahannock at Fredericksburg. I think he might here be underrating the difficulty of moving a large force quickly across a river by shipping - it's doable, if you have enough ships, but the loading and unloading consumes quite a lot of time. About two thirds of Grant's post-Cold-Harbor army crossed the James by steamer and that took about three days by my understanding, which is about two of McClellan's 1862 divisions per day. Even if three divisions can be moved per day, that's still four days to move the whole field army, and so it's at least a few days before McClellan can apply his superior strength to Fredericksburg - which is, well, Fredericksburg and thus a strong position. All Smith (IIRC it was Smith in command there) would need to do would be to wreck the bridges as the Union army approaches, and that's days of delay for Johnston to reunite his forces - though it would certainly turn Johnston out of northern Virginia.
So the Fredericksburg route avoids multiple direct attacks on Confederate positions north of the Rappahannock, but it doesn't solve the really hard bit of the campaign, which is the overland south of the Rapidan. The Rapidan and the lower Rappahannock are a really logistically strong position, mostly because of the Wilderness.