Problem 1: if you just take on easy fights, your Battle Rank (BR) goes up but you don't get many skills. The big enemies' powers scale up as your BR goes up so, if you do this a lot, the big events in the game start getting really hard. Use your ability to chain multiple mobs together into one fight to keep the battles challenging and you'll be fine. (You'll also have a lot more fun along the way.)
Problem 2: People who are not in your party yet don't advance. If you go slaughtering everything you see then respawning the area and doing it again, you'll start finding that the new folks you're hiring are pretty far behind everyone else. You'll end up with, I think, 18 characters so, if you spend 8 hours early in the game just levelling up Rush and David's little group, you can find yourself in real trouble. Your original characters will be high level, the bosses will be stronger, but the new hires get creamed and can't help much. (This isn't nearly as much of a problem in the last half of the game and isn't a problem at all once you hire everybody you want.)
The second one is what gets the "traditional grinders." In most RPGs that introduce charaters over time, the characters automatically adjust to match your level when you first meet them. Enemies, however, are fixed. Last Remnant switches that around.