You just have to play smartly to avoid grinding. There is always a mechanic that can be used to win battles easily, like abusing limit breaks or junctioning death to your gunblade attack. If you want to kill optional bosses or clear areas, you will have to grind. But if you just want to finish the game, just doing the side quests should get you to a level appropriate to defeat your enemies. You will have to fight repeatedly at times to get some spells or weapons, but it isn't as bad as you make it out to be.

I played only FF7, 8, 10, and 12 though, so I cannot really speak for the older ones. FFX in particular was way too easy to over level. I one shotted the final boss after killing a bit in the optional dungeon.