Moving across Europe may be harder than moving across the US. But moving across Europe (at least the EU) today is much easier than it was 40 years ago, pre-EU.
The bureaucracy can be a nightmare. Ironically one of the best country to move to pre-brexit was the UK. I did that without a lawyer. My other moves across EU needed a lawyer to sort out the local applications and required months ahead bookings.
I also had all sort of stupid issues which prolonged one immigration situation for 3 years.
I complained to the EU the host country was in violation of EU rules and they came back after 2 years saying it was my problem and that the host country was free to do whatever.
The EU is an absolute joke and a bureaucrauts' dream, no wonder our economy shrunk to half the USA's in the last 10 years.
I agree, it's definitely much easier than it was. But when comparing EU to USA and asking 'why', I think it's extremely important to remember how much less of a single market Europe is than the US/China.