The U.S. has them, not because of data protection in the U.S. but because of EU enforcement. All thos will do is change the legal basis and likely keep the cookies
This is the most important point. The EU is big enough that a large proportion of the world has put the cookie popups in. Whether they have done it right is a matter for a separate argument. The UK changing its laws isn't going to change any of this. The only thing it can do it give the bad consequences - the UK isn't big enough for this change to actually cause any good consequences.
The solution to the problem of loads of web sites making illegal cookie nag-screens isn't to relax the laws so that they can legally steal our data - it is instead to actually prosecute for the nag-screens.
The U.S. has them, not because of data protection in the U.S. but because of EU enforcement. All thos will do is change the legal basis and likely keep the cookies