Depends on the character design. I can't project myself into the character I'm playing, more power to the people who can, but I always considered myself as a player and the game doesn't work without me yet I don't necessarily feel like I'm part it's systems. Though I mostly create female characters because I don't see them that often.
I played Bloodborne with a female character because of how the armor looked, and a male character for Skyrim for the same reason. Mass Effect with a male Shepard because I felt like they put more effort into the design and I frankly saw him more often in the trailers.
Dragon Age Inquisition was interesting because the character design was good and it let me create an androgynous male character when I first intended to make a female character. The game was a little shite though.
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