I think the Bernardelli Baby was available in .22LR and was probably close to the same size as the Baby Browning. I would venture a guess that designing such a small pistol in .22LR would be rather problematic given the tight internal dimensions, variances in rimfire ammo, and the close tolerances needed to make it all work properly. The Beretta Jetfire design may not have been adaptable as such so Beretta came out with the slightly larger Model 21A Bobcat to accomodate the .22LR cartridge.
In comparison my Beretta Model 70S, built on a somewhat larger medium size pistol frame, has been totally reliable with any and all .22LR ammunition.