No government wants to lose all its people - since without people, there is nobody to tax.
In fact, giving up US citizenship is already made rather difficult - you typically have a huge tax bill to pay, and many people cannot afford to pay it, so cannot leave.
Trying to restrict the free movement of citizens here would throw the country into hellish anarchy, why would any “power that be” attempt that? The cost would wildly exceed any benefit.
If anybody in such a society wants to get anything done, they have to build a coalition and sell others on the thing they want to do. This is a very, very good thing.
Aside from “privatizing profits socialize losses”, why would the government care about fewer people paying the same percentage of their taxes? That makes no sense. Their budgets would contract with the demands.
Plenty of reasons people might want to leave a country en-mass, and some of them can't be fixed with a new government.
This is already somewhat of an issue for American immigrants moving to Europe. Some banks just refuse to open accounts for them.