Kind of late to the party, but constraints breed creativity rather than stifle it for the most part. It's commonly seen with the case of open ended toolbox games, lack of constraints produces simple archetypes and media-knockoffs, constraints(where there is SOME flexibility in deployment at least) produce a challenge, to create something new within the limits of the old and in the process synthesize into a more innovative thing than either the player or writer can envision in a void.
This is absolutely correct. However, the restriction can come in many different ways.
You can restrict yourself to making it fit a certain piece of fluff, which isn't a bad way to do it. You can also have a good game mechanic in mind, and create the fluff for it. When you have to explain the fluff of an unusual set of mechanics, it can make you very inventive. You can also have a specific in-game purpose in mind for the class. When that happens you have to be creative with the mechanics and the fluff can take unexpected turns.
Barbarian is based on berserkers, with the mechanics and the game role deploying that story.
Warlock is based on at-will magic, with the fluff and role made to deploy that mechanic.
Chameleon is based on the idea of imitating different classes but not all at the same time, with the mechanics and fluff deploying that game idea.
Basically, you do need a foundation but that foundation doesn't have to be a story.