It was the forage cap that was intended as an improvised bucket. The kepi is not nearly as deep as the forage cap. Though the construction is similar in that they both have adjustable chin straps and a hard disk on the top, the forage cap is much deeper and floppier and more field-practical persay. The shorter stiffer kepi (often with a shorter brim) was a knock-off of the French pattern cap of that name, more snappy in appearance (think dress parade) but used in the field nonetheless. Both types supplanted the regular army issue full-up dress shako for campaign deployment. I'm not sure many volunteer units were ever issued a shako, which was a kind of a holdover from Mexican war uniform by CW's start.
btw, unit designation brass symbols, letters and numbers were initially issued with the shako, only finding their way onto kepis as men went into campaign. Less so on forage caps and even less on slouch hats.
Today there's nothing more "farby" looking to authentic-striving reenactors than to see a slouch hat loaded up with the full cluster of brass. It's like "give it a rest." Look at period images and typically you'll see that even kepis have less that a whole cluster of brass, much less forage caps and even less slouch hats. (We reenactors commonly see a full brass cluster on a "wavy-rolly" slouch hat brim with the knot dripping off the front edge of the brim, not unusually accompanied by big glasses and wrist watches !).
The idea that the M1858 Forage cap was to be used as a bucket or even for forage is mainly a re-enactorism. Forage and fatigue were used interchangeably in the military and as such there were "forage" caps going back to the inception of the US Military. The M1858 forage cap was the idea of Major William H French who at the time was the artillery officer in command of Fort McHenry. During this period the M1839 forage cap (wheel cap) had been discontinued and the only real forage/fatigue cap the men had were either the M1851 or M1854 shako. The men, for comfort sake removed the stiffening of the shakos "to wear them on fatigue", this was not uncommon, the Utah Expedition photographs show most of the soldiers had done the same to their mixture of shakos.
French found this incredibly unsightly and looked for an alternative, many of his peers requested going back to the M1839 cap, while McClellan upon observing the Crimean War postulated:
"....a police cap, without visor and of such nature that it can be folded up and carried in the pouch, or wherever is convenient; the Scotch bonnet, Turkish fez, a Greek cap of knit or woven wool, a flexible cap of the shape of the old forage cap---any of these would answer."
Report of the Secretary of War, Communicating the Report of Captain George B McClellan.
Due to the above, French advocated for a "light, comfortable, military" cap that was also cheap to produce. He had 4 samples made, one for artillery, cavalry, infantry and staff, with the appropriate color trim. He did not go through proper military channels, but when the samples reached the secretary of war, were approved and forwarded to the quartermaster general. General Order No 13, War Department, November 30, 1858:
"For fatigue purposes, Forage caps, of the pattern in the Quartermaster General's Office, will be issued, in addition to hats, at the rate of one per year. Dark blue cloth, with a cord or welt around the crown of the colors used to distinguish the several branches, and yellow metal letters in front to designate companies. For unassigned recruits dark blue cord or welt around the crown and without distinctive badge."
If soldiers were to truly forage in the field, the haversack holds 4 times the amount of a forage cap, in addition, the chinstrap would not hold much in regards to weight before either the strap or button thread would part. The forage cap chin strap is a two piece adjusting strap with loosely sewn leather guides and a strap buckle that would not bear much weight.
One could see a soldier stuffing eggs in the cap for a short trip back to camp, but this was not its designed purpose or intent, it was for the comfort of the soldier on fatigue or field duty. Below is a shako of the 6th Massachusetts, Co G and a very early M1858 Forage cap of a soldier in the 9th PA Co E, as you can see the M1858 has the regulation brass in the correct positioning of an early war regiment.