Lets see:
Witcher Series
Gothic Series
Two Words Series
Many more I can't think of at the moment I haven't played because I'm only interested in female protagonists.
Dragon Age Origins (II and I arn't speaking)
Mass Effect Series
Jade Empire (There may have been a heavy style for men and a fast style for women and a balanced style for both. I'm not sure)
Neverwinter Nights (2 an Obsidian Game, would you beleive!)
Knights of the Old Republic 1 and 2 (Obsidian!)
The Elder Scrolls
Most of the Ultima Series
Fallout Games
All infinity engine games except Planescape to my knowledge
Even Minecraft and Terraria allow avatar customization
Just about every single MMO ever
This 'selection' thing is some old relic from shooting games and diablo (and revived with borderlands)
From what I can tell 'pure mage' and 'pure warrior' are reserved for male archetypes while females get some hybrids.
It seems by my reckoning that if DSIII is an action based game it shouldn't matter so much about the characters irrelevant personal life histories, and if it is a true RPG then there should be some customization of basic details.
I mean if the industry leaders Bioware and Bethesda can consistently offer us the choice..