Could you give an example in 5e or pf2e where that's not the case? Because that sounds pretty much like skill checks (basic flexible rules with common sense) and then the specific scenarios.

In my opinion, pf2e does this very well. One instance that has come up for me (in 5e) is doing a chase. With the existing rules, you can just have them run with their base speed, or have them make an athletics or acrobatics check, and that'll work just fine (and is what I did) but isn't particularly fun. Pathfinder includes specific rules for chase sequences (https://2e.aonprd.com/Rules.aspx?ID=1210) that is much more thought out and engaging. As a DM, you're under no obligation to have to do these just because there's a chase going on, if it's spur of the moment base skill checks work in a pinch, but if it's something I can plan for or I'm already familiar with those "rules" I can do something much more entertaining.