I hoped the idea of treating other countries like a menu of resources had died out a century ago. These are PEOPLE.

For example...
Every doctor in the 30 countries closest to us knows they'll have more rights if they go to one of the other 29. That's what your vote did. OWN IT! https://twitter.com/LukeOzcarp/status/1250599965535006720

In other words.
Ending Free Movement because you only want "high skilled migrants" means you might not get as many "high skill migrants" as you had before, because the act of doing so makes you the country that gives their friends/family fewer rights, i.e. less attractive.