Actually they do. They can't just process your data without your consent. The exceptions where they can process your data without consent are (at least to my knowledge) legal obligation (for example processing your income to calculate your taxes) and public interest (for example doing statistics on households), both requiring some legal work before actually being allowed to be used without your consent.
Technically they can do so that they don't have to care about GDPR but then it also has to become public knowledge that they don't want to care about GDPR and it becomes the responsibility of the citizens to oppose such moves.
EDIT: Forgot to add that in this case it most likely would become part of the law so yeah, they wouldn't have to care about GDPR in this circumstance.
That's also not entirely correct.
You don't need to ask permission for cookies that are strictly necessary for your site to work. They can contain personally identifiable information (PII) but only to the extent that is strictly required for the functionality to work. If your "required" cookie does anything more than what is strictly necessary (such as collecting more PII than it needs or has built in tracking) you need to ask consent.
If you're using something like on premise tracking, like Matomo, then you still have to ask permission. There are some exceptions like if you don't use cookies and you don't track PII.
And just for extra clarification, if you are collecting PII (for example into logs) you need to ask permission even when you're not storing any cookies.