I think prices will rise overall once the now 16 to 24 year olds that grew up with the system get careers and start using all their disposable income to relive their childhood. That is what is happening with the NES, SNES, TG16, and to a lessor degree the Genesis right now. It happened with Atari 2600 about a decade ago as well. Like the NES/SNES some common games will become inflated, but for the most part the uncommon and rare stuff will likely skyrocket as it has on 8/16 bit consoles right now. Look at what PS1 prices do in the next three years, that will be the PS2 in about 10-years most likely.
You think the PS1's prices will go crazy in the next 3 years? My counter point would be if it was the cartridge based systems that were driving the prices, and that the same conditions couldn't be met with a disc based system. Will ps2 discs even work in 10 years? The disc as good storage has never been tested.
PS1 games have already started to rise, and yes, many of the people that grew up with the PS1 are now at the age where they are getting careers, mlre disposable income, and have yet to be burdened with family responsibilities so they will start increasing the demand for these games and the prices will go up. I have been trying to knock out as many PS1 games on my list for this exact reason.
In regards to discs working in 10-years, as long as they are well cared for and housed properly, there is no reason why they shouldn't work in that time period. Hell, I was buying music CD printed in the 80s up until a few years ago, and as long as the discs weren't completely scratched, I never had any issues with them. Sure, they won't last forever (nothing ever does), that goes for carts as well.