I see how this is true in general, but aren’t there special cases e.g. within the EU, between the EU and the UK, or when an employee moves country while still being employed, where simpler solutions may exist?
There are cases and/or ways where you can e.g. hire someone under a local contract without owning a local entity, but that doesn't scale much beyond that, and you'd still need to run local payroll somehow, and be locally compliant.
The one big thing the EU solves is mobility: any EU citizen can work freely from anywhere else in the EU. That's a massive hurdle to cross otherwise.
Beyond that, even between EU countries there are absolutely massive differences in labor laws, standards, etc.
And how is the situation when the employees come in from time to time (commuting across borders) but work the majority of their time in another country?
> And how is the situation when the employees come in from time to time (commuting across borders) but work the majority of their time in another country?
This is a gross simplification, but: You must comply with where you spend the majority of your time. Spending a few days/weeks outside of your homebase is normal (see: all business travel) and doesn't make you immediately liable.
That said, this gets really complex and murky when you think about e.g. nomads or people that really split their time between countries.