If you have a protagonist who is customizable, then naturally the developers would write the character to compliment that so I don't think it's true that it would always compromise a serious story. You don't put things into a game with no care, thought or reason behind it.....
Yeah, a character can be written to be blank and accordingly the story as well, but vice versa applies. A story can be stronger written because the creator had a very specific look for them in mind.
You're not wrong about star wars and especially dragon age (had amended my post) but you brought up that Kojima is not to your tastes, so the point I want to stress here is that I'm not saying having a character be a blank slate or otherwise doesn't automstically become the detractor of a story but rather the creators intent and strength of writing.
Kojima is very much an auteur and in the case of Death Stranding I think he had a very specific person in mind, and that he wanted us to think of that specific person when we played through the story- and considering the plot itself (halfway through myself) I'm unsure how customization would have added to this.
In the end I think a lot of times video game stories are undeveloped or so disconnected from the main characters particular background so it's a lot of ymmv if it was a choice or not, but I stand firm with death stranding's choice of Norman Reedus.
Sorry, I might be rambling; I'm on mobile and I originally replied to your post thinking it meant something else so meh