I think that ship sailed when websites started having to ask users consent for cookies. Now it's no longer "accessing a website" it's "interacting with a service." If they have to ask for consent to set a cookie, you have to abide by their ToS to connect to their servers.
I highly doubt that is legally the case. In situations when I have been in conversations with lawyers about this sort of thing they have been universally of the opinion that to be bound to some terms of service the user has to take an affirmative action to accept those terms. The action can’t just be expressing your cookie preference, and in fact in some jurisdictions (Europe, California? I think) the cookie regulations that gave rise to those annoying consent dialogs specifically say you can’t give a user a different quality of service if they refuse the cookies, so that would seem to undermine your argument somewhat.
