>What about the European system prevents that for the
employee?

From personal experience:

1. Less employment opportunities due to no VC funding, and risk averse mentality of entrepreneurs meaning next to no big EU SW product companies. That's why the best paying jobs in EU tech scene are mostly US companies, which also tend to be clustered in only a few cities in the EU, where housing is now a major issue.

2. Employment and tax laws. 100% cross-country employment across the EU is still not a thing, as every government wants taxes be paid in their country, so they have the laws and bureaucracy in place to make sure jobs and tax revenue don't leave their country, so living in a country while being employed in another is incredibly rare as an employee and not a B-2-B contractor.

3. The big one: Language barriers and bureaucracy differing from country to country means huge friction and risk when moving to a country you're not familiar with, along with the added overhead of learning a new language on top of having a full time job plus the challenge of building new social circles with a different language and culture. I've seen many people leave a country due to the culture shock, language barrier and isolation that lead to, despite them being friendly people and productive workers.

This might even be a fun challenge to deal with when you're young and single, but when you have a spouse and maybe even a child, things get even more complicated fast when it comes to immigration, finding a house or a job, especially if your spouse doesn't work in tech or any other career where English is normalized at work, or even needs their credentials translated and locally equivalated by the authorities to be eligible for employment.

I've met many expat couples where one works in tech and their non-tech spouse has been unemployed for months/years due to their education, skills and experience not being recognized in the new country. Some EU countries really love bureaucracy, credentials, and don't tolerate you not speaking the local language.

A friend of mine got laid off as part of his company going bankrupt with his last two wages going unpaid. The bureaucracy, letter bombardment and appointments in dealing with the authorities to try to recoup those two months wages, all having to be done in German, a foreign language to him(and me), makes the experience completely exhausting and I can feel he just wants to give up on those unpaid wages.

Imagine someone from Ohio having to learn a new language when moving to California and then another language when moving to New York. Not having to deal with bureaucracy in a foreign language for every state is a huge asset for the US and a weakness of the EU labor mobility. The fix could be easy, mandate English as a second language for bureaucracy in every EU country, but I can name a few countries (not the Northern ones) where I know they'd rather see the world burn than adopt English. It's one of the reason why the UK and Ireland are the top destinations for EU migration, at least that was the case for UK before Brexit.

4. Racism, xenofobia, discrimination and glass ceilings from the locals, when you come from the "wrong" country, have a "wrong" sounding name or the "wrong" skin color.