Will going after those sites actually accomplish much?
They'll just add a third option, "pay", which lets you buy access without them storing personal information (other than information they need to recognize paid users, of course). Almost no one will actually pick the "pay" option, so for most practical purposes it effectively reduces to either "consent" or "leave".
I'd be perfectly happy to see what effectively is 3 optionsn "pay with money" "pay with info" or "leave". Whether or not people choose the same option anyway doesn't matter, it's now a much more informed choice than before as it's obvious how much your information is actually worth.
Also, sites that can't be bothered to set up premium/paid access mihgt do go the LA Times route and block access in Europe which I also think is completely OK.
They'll just add a third option, "pay", which lets you buy access without them storing personal information (other than information they need to recognize paid users, of course). Almost no one will actually pick the "pay" option, so for most practical purposes it effectively reduces to either "consent" or "leave".