I have attempted to answer this, and cannot come up with anything I've played recently where there are modifiable player characters. In the last, say, 5 years, I have actively played a frog breeding game, where there is no identifiable sex to the frogs (just species); a hidden object game that was all from the point of view of a set character (whose presentation annoyed me because it felt anachronistic, but I don't know enough to be *sure*); and a 3 in a row with a half-arsed story game, where there are (literally) cardboard cut out characters that appear to be from the 'select a stereotype' half price bin, but there isn't a character that is me. So basically, I don't know, because I don't have anything to point at and say 'this' vs 'not this'.