I grew up with it as the norm, so I don't mind it at all. It is a little irritating when you are trying to do a puzzle and enemies keep interrupting that, but that is a minor issue IMO.
IIf you play the original versions of Dragon Quest 2-3-4 or Final Fantasy (1), within a dungeon every single random encounter matters, every player decision matters and a single wrong decision can be costly. There is also the luck factor, even if you're always making the right calls there is no guarantee that something won't go terribly wrong and that keeps things interesting. Playing Dragon Quest 2 can feel like playing a high stakes poker game with the odds staked in your favour (compared to poker), and that keeps things satisfying because you know that once in a while something went your way that could very gone the other way. Random encounters are supposed to wear the player down little by little and the player should have to make the right decisions and use his ressources well in order to make the most out of his progress through the dungeon, which he may not clear on the first attempt. All this, after proper pre-dungeon preparations.
I'm not a huge fan of visible encounter systems where you have to sneak up on enemies or hit them at the right time to get an advantage. I just want to battle and grind numbers, which is really what JRPGs are about at their core. Yeah random encounters are better. There, I said it.
And then... THERE IS FINAL FANTASY WITH HIS DAMNED PRE-BATTLE VORTEX EFFECTS!!!I don't mind them that much, depending on the game of course, but growing up I'm mostly annoyed at slow/long attack animations. I can bear with them but having like the summon that last 20 seconds and you have to see the animation everytime pisses me off