I disagree. In the storyline, the bosses are never too difficult to require Mascot, Dark Knight or Alchemist. A White Mage is a great healer by himself - and you don't even need him either.
On my first playthrough, I played ONLY with the standard dress spheres, Gunner, Thief and Warrior (yeah I was stupid) and only on the standard Garment Grid. I went through Chapter 1 and 5 doing absolutely no sidequests (I didn't realize they were gonna be over until they were) and overall did few sidequests in general. Yet, I made it through the entire game. Of course, I did have a bunch of Game Overs on my way (smurf Vegnagun's Tail) but it definitely worked in the end.
The one part I can say you have little choice is the Via Infinito. Since the enemies there can take you out even if you're on Level 99 with fully leveled Mascots, you're pretty much forced to pull out your strongest guns. But since it's still challenging nontheless, I don't have a problem with it.