I think it's a little dependent on the genre of game.
Sport games, Animal Crossing/Harvest Moon-alikes, Dynasty Warriors, Fighting games and other such games, ones that rely more on gameplay than story, can only benefit from character creators. For example, I absolutely love wrestling games for the creations specifically. I can go and watch actual wrestlers wrestler. But only in games can I see a four hundred pound four foot tall luchador with robot claws do a somersault lariat on Hulk Hogan.
The only genre that's a complete mixed bag when coming to this is RPGs. On one hand, There's the Fallout games, Pillars of Eternity and Dragonball Xenoverse. Great games made greater by letting the player be whatever they want. But then there's Final Fantasy 7, Hyperdimension Neptunia, and Paper Mario, which are completely great despite not being your own OC donut steel. ANd let's not even get into the middle grounders like the SMT series. Games with fully establiished main characters that you get to name and have a few options here and there.