The 375 never caught on because in the real world it doesn't do anything a 30-30 or 35 Rem won't do at least as well, except kick harder.
The Hodgdon manual manual lists a velocity of just over 2200 FPS for both the 170 grain .30-30 JSP and also the 220 grain .375 Win. JSP.
Obviously a cartridge using a significantly larger diameter bullet which weighs almost 30% more than the 170 grain .30-30 bullet, while achieving the same velocity, is a more powerful and more effective hunting round. It would be foolish and deceptive to state otherwise.
The .35 Remington has almost the same diameter as the .375 Winchester bullet at .358", but only achieves a bit less than 2100 FPS, and with only a 200 grain bullet.
The .375" Winchester is obviously a more powerful cartridge than either the .30-30 or the .35 Winchester. The main reason it didn't catch on in the 1980s is probably that the average lever action rifle buyer simply did not care. A .30-30 was cheaper and a deer rifle was a deer rifle as far as they were concerned. Also, if they wanted a more powerful cartridge in a traditional lever action, they could go to .45-70 or .444 Marlin.
Both the .35 Remington and the .375 Winchester are powerful enough for moose or elk, where the .30-30 is marginal.
So the .375 Winchester does indeed do something in the real world that the .30-30 will not do as well.
Also, the Marlin .375 that I owned didn't seem to have any significantly greater perceived recoil than the Marlin .30-30 that I owned. It was in fact a very pleasant cartridge to shoot.