Even though they were more "known" back during the NES/SNES era, I'd say a good chunk of Culture Brain titles featured mixtures of combat systems in a single game. Like, you can say nowadays you get games that are ARPGs with turn-based or ATB-esque systems incorporated into the action combat. Something like Magic of Scheherazade or Little Ninja Brothers had BOTH ARPG combat AND turn-based combat. Magic of Scheherazade is like if Legend of Zelda not only allows you to wander around a world map fighting monsters from screen-to-screen, but sometimes there are random encounters that whisk you away to a turn-based RPG screen where you, your party members, and troops (that you can employ via cash at towns) fight monsters in a sorta Dragon Quest fashion.
Little Ninja Brothers (and others in the series) is a classic RPG world where you go wandering a world map but have random encounters that whisk you away to a battle arena where it turns into a Beat 'Em Up where the goal to win a battle is to defeat a certain number of enemies, but then most of the major boss battles are classic turn-based combat.
Flying Warriors, which was side-scrolling action platformer with RPG elements as well as some battles fought 1-on-1 (like a fighting game) and others fought turn-based (like old school RPGs).
I kinda liked that experimentation. The games could've been better, but ideas in playing with different gameplay styles are something I wish we'd see more in gaming, especially RPGs.
I don't think it's THAT obscure. That's called Mr. Do! over here:
More obscure than Dig Dug, sure, but I think it's heyday was back in the early 80s.