Yep. These things happen in cycles. You've got a period where no one cares and prices are very cheap (SNES) and then spikes tend to happen as nostalgia-driven twentysomethings with new disposable income start buying back their childhood. It's starting again with the PS1 right now. Prices will just get higher from here.
That being said, I doubt that PS1 games as a whole will see the increase in average price that you've seen with SNES games. People who start hardcore collecting for the NES/SNES/N64 often go for full sets because they're relatively manageable (700ish for NES/SNES and 300 for N64), so even the less popular and more underwhelming games start rising in price because there's a limited number of copies of Super Bowling or International Superstar Soccer out there and more and more collectors trying to go for a full set. The PS1, on the other hand, has a huge library that suffers from a lot of shovelware bloat. PS1/PS2 full sets are possible but you're getting into thousands of games, so I doubt you'll see as many Sony full sets out there. Of course, that means that lots of rare shovelware will stay cheap because the demand just isn't there.
Also, being on discs didn't mean that everything was printed in higher numbers. There are still some games on the PS1 that are rumored to have less than a thousand copies out there -- it just depends.
You're 7 years late.
I think there's no chance of PS1 rising in price much above where it is now.
N64 came out later than the PS1 and has seen significant price increases and "hidden gems" that have risen in price and none of this has happened for PS1 or Saturn.
Look at the early longbox releases, which are probably some of the rarest to find complete in good condition, because the console took probably a year to really gain steam in the US, plus the fragility of those longbox releases is at least equal with boxes from SNES/NES games.
We have a retro game convention in town here and every seller I talk to says the same thing - nobody wants Playstation 1 games outside of the few rare RPGs and crash bandicoot games. Nobody wants it, they don't want to buy it. They can't sell what they have.
A lot of the genres being served by a large number of PS1 titles are still being served by modern games and being served significantly better. Fighting games, racing, third person shooting, FPS, 3D platformers, all of these genres are better served with PS2/PS3 to the point where there is almost no reason to go back.
Now don't get me wrong - i have a huge PS1 collection and I love the system.
But those same people who shell out $35 for Super Mario World because it's still fun to go back to and they want to play it are not paying $35 for Wipeout because it's a classic. Or Ridge Racer, or Crash Bandicoot. Nintendo systems are the only systems where incredibly common, pack in/system selling games go for $30.