I’m torn about them. On the one hand they free up the combat design to be as wildly different from the exploration as it wants. Which can result in really creative stuff. Favorite examples are Undertale, MegaMan Battle Network series, and Tales series.
But on the other they interrupt the flow of exploration, the music, you forget where you were by the end of combat and they can be very annoying if they happen to be common or just as you’re about to leave an area. The consolation prize of growing stronger with every battle only helps so much.
I think, it works kind of well in games where you’re able to enslave/recruit the random encouters (Pokémon, Shin Megami Tensei and such), as it’s then a surprise what you’ll find, somewhat like a slot machine.
But the way the more recent entries work in these series, that you find out what creatures roam the world by exploring, that kind of works, too.
More generally, I don’t particularly like the problem that random encounters solve. Which is that you’ve got sections of gameplay where nothing happens, so you throw enemy encounters into there. That also goes for non-random encounters.
RPGs do this and I used to enjoy RPGs as a form of escapism. But now that I’m doing more stuff in real-life, I want it condensed down in roguelike form, or I’ll just play other genres…