I've never quite experienced this exact ideal, but I've come close. And I've also been beaten, which makes the next time even sweeter when my adjusted strategies carry the day.
This turns the game into a bit of a puzzle. Despite your mentioning them, Final Fantasies have typically been very good at this, if you take the minimal/"easy" game path. Which does mean not doing all the extras, but as FF games get bigger and bigger via copy&paste questing I'm finding this is less of an issue than it used to be. (You can still do the "postgame" stuff if you're that into it.)
The Persona series also involve some skill and some luck; sometimes I find it hard to believe how one error can be the difference between wiping my party out without me touching the enemy and my wiping out the enemy without them touching me. It doesn't seem like it should work that way, but it has happened to me numerous times, where even a well-leveled party for where they are gets themselves wiped out because I had a momentary brain fart and hit the wrong command in the first round. It's a very mathematically unstable system, vs. FF's very stable/predictable one, but great fun.
FPS/RPG hybrids often have this, the most notable I can think of being Deus Ex (Bioshock is a passable example, but nowhere near as complex in the endgame). Action and strategy RPGs have this if played in a certain way, though most of them are just really easy to begin with. Roguelikes have this in spades. The combat in pen-and-paper dungeons and dragons can have this.
Console-style RPGs like the Final Fantasy and Dragon Quest series usually don't have this. MMORPGs usually don't have this as such; rather, they usually have two almost independent games (beginning-game and endgame).