The EU still allows transfering data to other third countries if suitable protections can be effectively put in place, whether through some governmentally agreed program like what Privacy Shield tried to do or through Standard Contractual Clauses. They simply view the laws in the US as too hostile to most of their residents' data privacy rights. ("Most" instead of "all" because US citizens have more protections under US law even when living in Europe.)
So, while sure it is a kind of border, it's a "privacy-protected vs privacy-dangerous" border rather than a blanket "us vs them" border. Or, phrased another way, it's not a border as a goal, but rather preventing the nature of the internet from overriding their separate privacy goal. I am fine with that attitude.
Let's take Facebook. We could have Facebook.US, Facebook.EU, Facebook.UK, Facebook.CN, etc.
In a borderless internet, you'd still be allowed to use the one that you wanted, but each would be subject to the laws of its "country". (I realize that the EU isn't a country.)
Plus it's not in $country is in $region, if all countries made an effort to adopt GDPR data could be stored anywhere.
EU is looking for their citizens data, since no one else seems to care that much (other than China but for completely different reasons).
Unless you think that the protocol of tech giants to poor data protection is fine, when they are saying:
"Ups, we're sorry :(... it won't happen again!"
Yeah that’s part of the original vision of the Internet.