Believe it or not, I actually used both for my late-game party lineups. Actually, I used both Hero and Dragonite since I got their second-tier growth plates, just so everyone has a unique weapon.

See, it's a habit for Exe-Create to give one of each "ultimate weapons and armor" just before the final battle so I wanted to make sure everyone had something unique.
I stopped using Priest and had Iria switch to Dragonite permanently around the time I got Elodia. Even though healing is still needed at that stage of the game, if you're good at items management, you can still survive even without healing magic. Plus, the Hero class is the only one (without switching to Soldier, etc) that makes use of Heavy Armor early, which is something that benefits Lucas more than Soldier anyway.
This was my final team lineup by normal end:
Lucas: Hero (Warrior and Hero classes both mastered, has all Sword Arts skills mastered)
Iria: Dragonite (Dragonite class mastered, has all Martial Arts skills mastered)
Melvin: Thief (Thief class mastered, has all Dagger Arts skills mastered)
Elodia: Mage (Mage class mastered, has all Staff Arts mastered)
But to answer your original question: it's because of "team balance" and ease of use that many prefer Lucas and Iria to stay to their first classes. I mean, every balanced party needs healing, but the game is honestly easy enough at normal difficulty (without mass grinding) that I never found Priest to be -that- necessary for all points of the game.
I can't comment much on the other classes, never did much experimentation outside the first four (and Hero and Dragonite, obviously). But I did love Hero because of its anti-dragon skills, very sorely needed for the danger area boss dragons as well as many of the bosses themselves. Also, Dragonite skills are very good at debuffing stats as well as AoE damage, and was very versatile in terms of attack options (there were some enemies that could nullify physical or magical, but never both at the same time).
Still, the auto-skills from the other classes are pretty nice. For me, I went for Merchant's auto-skills first to save on money so I could keep my stock of healing items secure

I actually have no idea how well the autos are for Mystic, Pharmacist, Soldier and others.