I create my own PC's fluff while obeying the rules.
Each class starts with three examples of the class in a brief description. These are just examples, not role-playing shackles disallowing your own character ideas.
My rogues don't feel compelled to steal from their own party, and rarely steal at all.
My barbarians are frequently wearing civilised clothes and have never slept outdoors before their first adventure. Few of them feel compelled to prance about in a fur loincloth.
Few of my monks wear a Gi or shave their heads. Some even wear a nice suit and work as a bouncer in a fantasy nightclub.
Tell me, what are 'fighters' like? Do they all behave the same, dress the same, have the same background, same motivations, the same....anything?If so, why would I play with a DM who won't let me create my own PC? If not, why compel this for ANY class?
ALL of the class mechanics are up to the player to fluff in any way that they can make plausible. Rage? Deity-inspired fighting trance. Bard? Joxer the Mighty, specialising in buffoonery, inspiring his party to greater heights to compensate for his perceived incompetence. Aasimar monk? Angel in human form who is a crimelord who is that hard!
The DM doesn't create the PC, the player does, according to the rules.