You're doing both.
In every functioning nation, the rich subsidise the poor.
I as an above average income earner am necessarily always going to subside the poor no matter where I live — unless it's a place that's got no government.
That was true when I lived in the UK, true when I moved to Germany, and would have been true had I moved to the USA instead — all that changed for me was Joe Bloggs became Otto Normalverbraucher instead of Bubba Sixpack.
> I don't care why or if you immigrate, but if you do
Except you previously wrote "How about door 3: only allow immigration for skilled individuals capable of adding outsized value to our economy?"
If you "allow" something but nobody wants to take you up on it, it's not any different than forbidding it.
I'm allowing people to donate infinite money to me, but I'm not taking any steps to encourage this or give anyone a reason to.
> People hiking across the Darién gap aren't magically going to become engineers and doctors
Likewise a degree.
In both cases the capability is already a demonstration of being well above average.