Yes, the bell-crown shako was much more of an 1820s-era thing... The hat at the auction house has a shako plate national eagle from the 1820s on it... Although presumably these were used as surplus when the slightly smaller eagle facing to the wearer's left rather than the right like on the 1820s U.S. eagle.
The bell-crown shako was a big deal in many European armies too... Including the British and the Swedish among others. It was hot and uncomfortable, so it was supplemented by a forage cap or fatigue cap of some kind. In the United States, the rather Prussian-looking pin-wheel Model 1825 "chako" or fatigue hat was adopted. It was relatively cheap, had a leather brim or visor, and piece of wire to hold the shape of the crown. It had an arm of service button on the top of the crown--white metal for infantry, brass for others like artillery and so on. Also the piping on the head-band was white or yellow. It is a rather comical looking hat, frankly. When shakos became more stove-pipe shaped again, the idea arose to replace the 1825 cap with the hideous 1833 folding leather shako or "hog killer." Because it was supposed to made of specific kinds of leather, it was to be both cheap and long-wearing, lasting up to five years if not more. It was the hideous and uncomfortable headgear of the U.S. soldier in the Second Seminole War in Florida, although I suspect many were fed to alligators and did not return... The West Point cadets had them by 1834. Between late 1836 and 1839/1840 some were used by the Texas Republic too. In the United States, the dragoon variant had a little button-up neck-flap, which was missing on the variant worn by infantry and the U.S.M.C. The only decoration was a pair of arm-of-service buttons supporting the chin-strap like a Civil War kepi or bummer and a single letter for the company. Some used by militia sported all sorts of fripperies like plumes and even shako plates.
By the U.S. War with Mexico, the Model 1839 "wheel hat" also often with a folding neck and ear pieces was most often worn, but certainly the leather shako remained the dress hat. I think the frontier experience of U.S. soldiery omitted the wearing of shakos except for parade ground use or fancy marches past and so on. A more pragmatic, practical hat was needed. By the 1850s shakos got smaller, and the British style and French styles proliferated. Some of the 1850s shakos, with the stiffener or wire armature or whatever to hold it up removed look just like a bummer... Somewhat ironically, when the "side cap" or "service cap" or "bonnet de police" came out, it resembled nothing so much as a pared down version of the late 1700s/ early 1900s fatigue hats made of excess uniform sleeve material..