So if technical constraints didn't stop Square from implementing Party Switching in FFIV, how much do you think would've been added/changed? Square was supposedly implementing party switching for FFIV, which explains why a lot of the characters survived and were waiting at the tower of prayers.
Obviously, party switching would be implemented. As well as the Cave of Trials (or an equivalent of it, since otherwise Yang, Palom, Porom, Edward, and Cid's best equipment would suck compared to the final five's). But what about the Lunar Ruins? It was also mentioned that Square wanted to have a dungeon where each character would undergo a unique trial, a concept that they couldn't implement in FFIV SNES, but they implemented in a game called Live a Live or something like that. If they were to implement that kind of dungeon in the SNES version, I doubt they'd make it as big as the Lunar Ruins or have any superbosses there.
Come to think of it, regarding no Cave of Trails equivalent, Palom and Porom would still fare well equipment wise. Cid would have access to decent armor with Dragon equipment, but no decent weapons. Yang would be the opposite since claws add accuracy instead of damage (well his body armor would be bad, he could still use Ribbons and Protect Rings). Edward would be really bad body armor wise and weapon wise (unless you could find or spare him good bows and arrows).