I’m surprised you mentioned the clock in ratchet and clank 2 but not the insomniac museums. There are portals in ratchet and clank 2 and 3 in kind of obscure spots (on top of a fountain on planet boldan in 2 and off the main path by some chasms in metropolis in 3), and they do nothing most of the time. However, if you stand on the portals at 3am system time, the portals activate and you can go to the insomniac museums. They have things like concept art and places the devs used to test vehicles and all sorts of weird stuff.
Calendar Man in an Arkham game has things to say on specific dates There's a dating sim for Saturn that uses it to tell how long it's been since you interacted with the girl last, and she gets annoyed if it was too long
I always thought this was an underutilized mechanic in games. Considering how effective it is in Animal Crossing, it's weird how only a few other games actually use it.
I can remember right before MGS 5 came out it was rumored that it would have a 24 hour cycle so that when you played the game in the real world that's the time it would be in the game, it would've been something unique but probably annoying at the same time, if you could only play the game at night for some reason like a weird work schedule you probably wouldn't want it to be night time every playthrough, it could've worked if you had the option to turn it off if you didn't like it though.