I don't see any problem with the cartridge itself, OR the rifles other than possible the cartridge belt, which is a problem with the PERSON rather than the cartridge...and maybe rifles with short magazines where you can't seat a heavy bullet out unless you single load it.
ANY of those problems can be solved by going to the WSM case, which, as time goes on, will probably happen to make things easier. 350 RM cases will ALWAYS be available even if you have to reform a longer belted mag case to get there.
I always liked that Remington 673 but never got around to buying one nor ever got into the 35 cal until I had a Marlin 336 rechambered/rebored to 356 Win a few years ago. I had a Rem 700 rebarreled to 338-06 back mid 60's, then jumped to a 375 H&H, but I think the 35 cal is just as good as the 338 or 375 for the most part, and the arguments of one over the other are really just nitpicky personal opinions like we all have.
If you have one, cherish it...if you want one, better hurry up and buy one. Once something is discontinued, the price soon jumps and the auction block seems to be the coming thing.