I understand the point of convenience, and having discussions and changes on implementations is good, but there is a reason that the law targets websites and why the whole discussion is around websites rather than browsers: the websites (their servers) are those who actually collect the personal data. The law does not target browsers because the browsers (their companies or whatever) are not the data controllers in this case, the website owners are.
Moreover, consent by law tends to need to be specific: you give consent for the specific purpose to the specific company. Of course there are and should be ways to convey denial of consent by "do not track" style headers, but I am not sure this can solve all the issues.
I think blaming the law is bullshit. When a website throws a cookie popup obstructing you from using it, it is because they really want you to click on "accept all". There is no other reason to do this. It is terrible UX and not all websites do this. It is a totally conscious and intentional decision.