Actually I would think it a lot better If the class you picked determined your starting stat bonus and equipment. Maybe +1 based on each ability or just make starting stats a straight buy in that you choose.
I always added some reasons when adjusting stats for a race for my players in D&D. So you're a dwarf but maybe you were a little undersized and picked on so you spent your time alone studying the arcane instead of doing whatever it is young dwarves so.
