What this gives the EU is the hammer to hit persistent abusers of user data. They want you to be careful with user data and not treat it like you own it; you do not. It is not yours to sell or share or publicize.
Edit; note as well that every country has a compliance office; if they know you are in complaince as in you are ‘good people’ (best effort, no giant holes etc; just best practice in our field which you should do anyway) they will not bother you with every (or any) user complaint after that. I have good experiences with this with far grave (and potentially criminally punishable) matters in a few EU countries.
No its not as they now have regulations in place to prevent that, before GDPR you could. You can only be sued to the poor house from it if you do something like leave your patients health information on the bus.
The regulator is the effective judicial remedy.
In the UK there's also a First Tier Tribunal and probably an upper tribunal. These are when the regulator has made an error in law.