Familiar Spent .22" Rim-fire Case
There are more than a few rimmed centre-fires used in 'autos' too - such as the Colt 1911 in .38 Special and both 357 Magnum & .44" Magnum are used in the massive 'Desert Eagle' .. many older auto-rifles ran on rimmed cartridges.
1911 Magazine for 38 Special.
Target pistols used to often come in .32" S&W wad-cutters & .22" rim fire options
Hammerli Model 280 takes either .32" Center-Fire or .22" R/F.
While the rimless pattern may be better suited for a self re-loading mechanism to function reliably, - it is possible to build and refine just about anything until it will work: "If you can imagine it - You can make it."
One further small issue with rimmed (& tapered) rounds in autos is NOSE-DIVE .. As the base of the top cartridge in the mag is pushed forward to be chambered - it's nose can dip down and then impact the metal below the chamber opening and jam.
This can be fixed by adjusting the feed lips by squeezing or bending them slightly until that magazine behaves itself. - Other cartridges, despite being rim-less, can be liable to nose-diving, particularly the short'n'fat .45" ACP ... you can even buy specially made 'anti nose dive' "Sure-Fire" magazines for your 1911 from Gun-Pro.
P.S. Another issue with rimmed or tapered cartridge cases is that the magazines properly need to be curved .. such as the iconic AK 47 shape"
but there may be other design priorities eh ..
Some "Straight-walled" Cartridges such as the 9mm Bergmann / Bayard / Largo (and the 9mm Parabellum) actually taper around 12 thou. to the mouth. ( The Russian AK 7.62x39 rounds also taper a fair bit - which is why they use that distinctive curved magazine .. it is of course, a rimless cartridge).