And a semi-auto magazine fed rimmed cartridge would be a pain to design and keep running.
Like the .22LR??
Desert Eagle and Coonan have pretty well shown it can be done in .357 Magnum. The SVT40 (and others) have shown it can be done in rifles. The BREN gun (and some Soviet designs) show it can be done in a LMG.
Feeding a rimmed round through a semi or full auto action is not the virtually impossible task many make it out to be. Yes, it takes a different and more complicated approach than a rimless round, but it can, and has been done, A LOT!
The main problem with designing and making a semi auto .357 Mag carbine is essentially there is no demand, and no matter which way you overcome the engineering challenges, you aren't going to please everyone.
Low demand, because there are so many other choices currently, that cover the niche the .357 fills in a carbine. I don't see how you can build a semi .357 carbine with the easy handling lines of a lever gun AND a 10 round detachable box mag, that people would accept in terms of looks, performance AND COST.
You're welcome to try, maybe you can make it a viable proposition. So far as I know, no one has, so the field is open. Good Luck.