I don't see any real role for pyro, he kinda sucks at everything. Well not exactly, he is great at being AFK near a dispenser spy checking, removing sappers and airblasting stuff away, so if you want to play turtle he is ok, but if you're on offense or just want to play for real he is trash.
He can't do good damage at midrange like Demo and Soldier.
He needs to hug enemies to kill them, but he isn't as fast as a Scout or survivable like Heavy, so he feeds super easy.
And the flamethrower's damage isn't even all that good, if you don't surprise the enemy and do good damage before they shoot you you're not killing anybody.
I see him as the worst class in the game overall