Privacy is an excellent example. At first it was locally dealt with, and big tech would lobby the individual countries for all kinds of exceptions and ways to effectively get regulatory capture. Then, in 1995 the EU created the DPD.

https://en.wikipedia.org/wiki/Data_Protection_Directive

Big tech and the advertising industry responded by sidestepping the new regulation to make deals with the individual countries to undermine it, and actually managed to get close to getting their way, and possibly to get it repealed completely.

https://www.nu.nl/internet/2849758/druk-van-lobby-opstelten-...

But the EU responded with the GDPR.

And now big tech is again lobbying and pressuring member states for exemptions, for example, Facebook:

https://www.theguardian.com/technology/2019/mar/02/facebook-...

This is just venue shopping, can't get what you want in one place then you just fragment it and try to get multiple smaller deals. So I totally expect a similar thing to happen around this subject, the stakes are just too high for them to ignore the whole EU for their games.