OP, I actually had this idea recently while doing a quest. Since a lot of the quests are running around, it would be neat if while doing said running around, you were forced into battles. There is an Ixali daily quest that causes a mob to spawn on you while you're doing it, but you're not required to fight it and you can simply just run away from it and it will despawn. I also recall in Everquest 2 there were quests that if you had accepted them, it would cause mobs to randomly spawn on you in certain areas - even if you were already fighting.

To really give it the Final Fantasy feel, I don't think any teleportation into a different screen like single player FFs is needed, but getting into a random encounter could simply place a battle zone ring area around you that you can't exit until all the mobs are dead. And yes, like you said, it would be nice if there were mechanics and increased AI and difficulty.