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.
Not every design choice fits every game (obviously). With that in mind, rarely is any specific design choice always 100% good or bad.
I think rather than just taking a vote, it is more useful to think about what makes a good random encounter, and what kinds of game designs work well with them.
I enjoy CRPG styled games. Often in these random encounters happen when moving through an overworld. This kind of design doesn’t disrupt exploration, since once it is over, you continue on your way. It does disrupt when you are going between known points and just trying to tie something up. That can be annoying. Ways that I think can make random encounters enjoyable for CRPG styled games:
Not every random encounter has to be combat. Some can be combat, some can be social, some can be vendors, and some can just be flavor. Non-combat encounters can be used as sort of optional bonus content for players to learn about the lore or explore, and they might even feel special since it is a random occurrence the player gets.
The ability to put points into some kind of skill that gives the player the option to avoid a random encounter and/or start a combat encounter with a bonus.
Encounters should be tied with regions of the overworld in a way that makes sense. Put tougher encounters in endgame areas to discourage players from poking around too early. Make encounters in certain areas tied to the main faction or location in that area.
Ease up on certain kinds of encounters as the game goes on, so they don’t outstay their welcome. For example, in the early game if there are lots of low level bandits attacking in random encounters, it can be fun, but it gets old once you are powerful enough to rip through them and are just trying to get bigger things done. Solve this by, for example saying that routes between major hubs are secured thanks to player actions. Now the player can travel between main routes without getting hassled.
Be very thoughtful about combat random encounters triggered by NPCs after the player due to player actions. These tend to be more annoying since these are usually higher level NPCs that pack more punch. Making their appearance totally random can be very annoying. It also often feels like a grind if the encounter happens repeatedly. I would prefer the consequences of player actions to firstly always be telegraphed so they know a certain action means a revenge squad is after them. Second, I would prefer this encounter to be scripted- either concretely in a specific location where the game knows the player hasn’t yet been by virtue of the trigger happening while certain areas are still locked by the main story, or in a floating fashion where one of various possibilities is chosen by the game based on whatever triggers first. Once the player defeats whoever is after them, they should never be chased by an identical kind of threat.
These are all CRPG ideas, but I think mostly translate to action RPGs conceptually.