The point of that message wasn’t that anyone can literally be Spider-Man. It’s that anyone can choose to do the right thing. Peter is just like anybody else but this great power was thrust upon him. He acted like a selfish dickhead at first, but learned the weight of responsibility that came with this power.
The problem for me is how Marvel and by extension Insomniac misinterpreted that message to Spider-Man into a brand while putting Peter Parker, the driving force of the character, in the back seat (if not outright shoving him out of the car).
TBF, when Stan Lee was talking about Spiderman and that 'anyone' could be him, he
did actually allude to who was under the mask, too. Not just whatever the person engaging with the material happens to be.
So I guess if anyone can pretend Spiderman is any color (or even a different gender) under the outfit, by extension they can picture them not looking like Peter Parker out from under the outfit, too. And like said in the clip, that wouldn't have been through an intentional design choice by Stan & Kirby back in the day, but something does tell me they'd be a lot less apprehensive towards making someone like Miles Spiderman than some of the people I've seen online upset by it.
Which is wild: when the actual creators are more willing to accept something than some of the fans. Of course, it all comes down to the reasoning and if a replacement were say poorly written, then it stands to reason that Stan, Kirby etc. wouldn't want them as the new Spiderman either, exactly because of poor writing. Then you'd see the fans who only care about representation above storytelling throwing a hissy fit :/