For me it's different, I end up getting into the character, and I end up being myself
It's pretty clear these games are built that way, putting you in the main character's place. You know, like VR porn?
But seriously, I think that's the whole idea about the whole 'name your characters' deal. Not a new concept really. Many great fiction novels of the past, some quite erotic, were written for the reader to immerse themselves into the story. In essence put yourself in the place of the main character. Over the years that writing style would continue through all forms of commercial media, movies, radio and TV. That's where the descriptive phrase "tear jerker" comes from.
However for me, it takes a really good story for that to work. Stories that weren't to my tastes would be the books I'd never finish, movies I'd shut off or walk out on, and now in this genre games I wouldn't bother finishing. I've skipped over many a game with really hot characters and great renders with no real story or a real crappy one.