Honestly, when you only have one character, turn-based combat tends to be rather boring. You simply just don't have that much to manage that a turn-based abstraction is now adding anything to the combat, and the detractions (and slowdowns as you now watch the enemy take its turn one by one SLOOOWLY) start to dominate. The only games that really do solo and turn-based well are games like Nethack. Most other games are just too simple.
I think TOEE was hard to beat here.
Prolly still JA2 1.13
This probably really did sorta peak with Diablo 2.
No RPG has ever done first-person action combat better than RPG-7. It's totally realistic, tacticool, and when you die in RPG-7, YOU DIE IN REAL LIFE!
But other than that, I can't think of too many RPGs that are firmly both entirely first person AND firmly action combat. Maybe Deus Ex? But I wouldn't say the combat was GOOD in Deus Ex. Every other game tends to have a third-person view, as first-person melee is not generally a great experience. Except RPG-7.
I assume by "not round-based", you mean, "has a time resolution lower than an actual action", since pretty much all games are tick-based simulations rather than continuous ones.