The short-term effect of GDPR is ugly interstitial pages and mandatory consent, but that's not the point of GDPR. The point is to make legally collecting user data difficult, annoying, and onerous in the hope that going forward more companies will eventually decide it's more trouble than it's worth. That'll only work if complying actually is a chore.
Call your local news site and complain if they aren't honoring GDPR to the letter. Call your country's ICO and complain to them too. Talk your friends and family into doing the same. Be a pest; the more annoying the better.
As a matter of fact, I do complain a lot, and I do file complaints about GDPR violations, but convincing my friends and family to even care about this stuff is science fiction (I've tried for over a decade now without success).
Business and engineering culture around website construction is horribly broken with regards to user privacy. Changing that culture is going to take years of consistent pressure which existing interests are going to fight every step of the way.
In my opinion the ugly consent forms are the best thing about GDPR. A problem that techies have known about for years is now visible (and annoying) to the general public. Of course that doesn't restructure the entire internet overnight, but dragging the problem out of the shadows seems like a pretty good opening salvo.