The issue is some sites won't display any content without cookies, even if it's unnecessary. The amount of React-using sites that will load the entire page only to a second later to fully blank out since the JS couldn't set local storage does get annoying (and can regularly be worked around by disabling Javascript if not used for anything substantial). A handful like this have appeared just this past week on the HN front page.
Example: The identifier you get when you pass anti-bot challenges (Cloudflare, Anubis, etc).
Whatever mechanism they choose to uniquely identify you, they will insist it's necessary for another purpose and they totally are not piggybacking on it for tracking (e.g. for the CAPTCHA example, they would insist it's absolutely necessary to protect themselves from DDoS).
As another example, they can always respond with HTML where all links themselves are an opaque hash that internally contain "route + your id" when decrypted. Then emphasizing that all links are always different even for same routes to "show they are randomly generated", and saying that they do this because... idk, detecting scraping or something random but plausible-sounding. Or whatever sneaky variation of the `?PHPSESSID=` query param from old times.
(Yeah I know the last example doesn't a lot make sense, I didn't think too hard about it, the point is that they will probably find a way somehow.)
The annoyance of the cookie banners is the entire draw for companies. Its not a downside. They're user-hostile. You are their enemy. Their goal is to wear you down and trick you into opting-in, so they can both track with impunity and follow the law.
I know, that is why I am saying you would force them to respect Do_Not_Track by law.