The first year or two of any new system launch generally doesn't have paradigm-shifting game design choices that absolutely require the next-generation hardware. Indeed it took until late '96 or such for the PS1 to start seeing those kind of games such as Tomb Raider and Resident Evil, and you can see that pattern repeated with virtually every other PlayStation console and portable device.
I don't know, you said this in another thread, I think you're discounting too easily what new hardware has historically brought even on launch day. What your and my arbitrary line of a "paradigm-shifting game", but there's always something "new" about next-gen titles from the get-go. There's a magnitude of scope, a level of effects, and a slew of rendering techniques that are easy to take for granted when you're expecting miracles and getting only a slice of the future (especially when you have PC games kind of evening out the transition, also consoles in the middle like Dreamcast,) but when you look back, the transition is clear. And especially once you leave launch and start getting those March and Summer titles that they let cook a little longer, the difference widens out; by the time you get to that first Christmas after launch, past-gen looks like a distant and ill-remembered memory.
Often developers play with things in those early days and try out tech that is neat but not really practical going forward. Even something like Fantavision, that was a particle tech-demo made into gameplay, and you could make a fireworks game if you needed to with PlayStation, but that kind of particle system was made possible because of the new hardware.
I mean, just taking the PlayStation as an easy-to-track generation, look at these games, then look at the games from generations before at even their best, and it's pretty clear that current-gen was past-gen the day the new console arrived.
PS1: Ridge Racer, Wipeout, Air Combat, Toshinden
PS2: Tekken Tag, Dynasty Warriors, Kessen, Dark Cloud, AquaAqua, SSX, Smuggler's Run, TimeSplitters, UT
PS3: R6 Vegas, Oblivion, Untold Legends, Blast Factor (not revolutionary in and of itself, but you couldn't download games with PS2, and now you can)
PS4: Knack, Killzone Shadow Fall ... not much at launch.
PS5: nothing confirmed, R&C Rift Apart is perhaps only game so far that's "not possible" in a real capacity on PS4
And also, perhaps the gameplay always takes a while to really harness the new consoles, but graphics are a huge part of games, and graphics always step up immediately. Once you transition over, it's always difficult to look back and find the past-gen acceptible any longer. Jaded gamers like to LOL when new consoles came out and had a lot of familiar names and playstyles on the new boxes, but even though CoD or Madden are still mostly "the same game" in the transition, the difference to somebody looking backwards is enough to never look back again.
(Replaced the video, at nush's request. Unfortunately comparison videos of either FIFA or PES over the years tend to also have a lot of talk, but this one goes all the way back and shows lots of goals.)