It would have changed a lot of things I think. Though I disagree about the PS1 era being held off until the Dreamcast as part of the reason why Square jumped to PlayStation was because they wanted to move beyond cartridges to expand the games. Sega never had that problem so I'm pretty sure the PS1 FFs would have appeared on the Saturn or even Sega CD depending on the game.

Honestly, I feel it would have been bad for everyone. The Seaf systems wouldn't have had the power to make impressive games like VII- IX and so them being on the Saturn wouldn't have saved that poor system, Sony would lose another killer app and probably be in a closer competition with Ninetnedo, and Sega's implosion was less about making crummy consoles no one played (despite what people think the Saturn was actually fairly popular from a global sales standpoint) and more to do with terrible management of the companies resources which caused them to burn money faster than they were making them. Hell part of the reason why the Dreamcast failed was because not only did Sony do a pretty great marketing campaign for the PS2 but at the time of it's release, it was the cheapest DVD player on the market, a strategy they tried to re-use with mixed results with Blu-Ray on the PS3. So FF would have probably jumped to Sony eventually regardless and RPGs were not a strong global market in the early days to make much of an impact. The big change would be that the PS1 games would have probably looked less interesting on the Saturn hardware and would have made far less of an impact. We probably wouldn't have had the RPG Boon in the late 90s for console RPGs. Of course this is all speculative...