I don’t think fixed or open protags have anything to do with the level of an if interactive scale nor does it determine if the quality of the story is good or not because of one or the other… its all about how the author utilizes the two concepts . i also disagree with the whole black and whitening of fixed and open protags. they tend to sometimes overlap. a story can have an open protag that is already fixed in some ways.
example. player chooses race gender and all that comes with a standard character creator. player then gets to choose things like origins that makes them fixed and established in the setting. the narrative then sometimes remembers set origin and might even do something with it.
games like choice of magic and the infinity series does this very well.
also open protagonists can have depth to them if you try to write them that way. instead of writing them as if they are in a simulator game .
the problem with open protags in most cog|hg is that they drop you in the story rather than fist making a character a part of the world through player choices before they then process to thrust you into the story.
by and large people don’t want the author to rewrite a character for their own joy. it just that people tend to sometimes suggest to the author that they should allow multiple player styles since the the author has established that the player is an open protag like @MeltingPenguins said
