John Browning let us down here.
That's hardly a fair statement. You may think Browning "dropped the ball" with semi rimmed cases, but are you aware that at the time, nobody knew what the best shape for the ball was, nor were they even certain of the rules of the game!
Browning designed the .32ACP in 1899. The .38 Auto in 1900. A bit BEFORE the 9mm Parabellum. A time when no one was certain that a case headspacing on the case mouth would reliably work. Browning knew the semi-rimmed case would WORK, and work in an autoloader better than the fully rimmed case. So, that's what he designed.
A few years later, when Browning designed the .45ACP, in 1905, he did make it a rimless case, because the concept had been proven to work. (9mm Parabellum, 1902)
The .38 Super came along in 1929, and I suppose you could say we were let down on that one, because it was semi-rimmed, but that's really just 20/20 hindsight. The Super kept its "parent" case. The only change from the .38ACP was an increased pressure loading, the name, and the marking on the case head. And usually nickel plated cases for the Super.
I just can't imagine a semi-auto handgun can feed a rimmed cartridge as reliably as a rimless one.
Perhaps not, but its not because of the fact that rimmed rounds won't work in autos. Rimmed rounds work fine in autos, PROVIDED the guns are properly built for them. There are literally dozens of designs of machine guns made to use rimmed rounds. The two biggies are .303 British and 7.62x54R Russian.
And then there is every single semi auto .22LR in the world, all using a rimmed round. There are two main factors at work determining the reliability of a semi (or full auto) running a rimmed round. First is the design itself, and second is the execution of the design. Which is where most have their failures, if they have failures.
The action might be perfectly fine with rimmed rounds, but if the maker pairs it with a cheap piece of crap magazine, problems happen. And when problems happen, its the rimmed round that gets the blame.
I've heard about issues with rimlock in .32acp, and while just as possible, I've never seen any reports of this trouble in the .38 Super. It could happen, but no body has made a big deal out of it, as far as I can tell, in all the decades since the round was introduced. The only thing that seems to be in the old literature is how the Super's accuracy was spotty, and when barrel makers began headspacing the Super on the case mouth instead of the traditional method using the tiny rim, complaints about the Super's accuracy basically went away.