They allow brain drain to happen, without the barriers of having to move countries.
The amount of money I poured into the local economy is probably an order of magnitude higher (maybe even 2) than if I had worked for a local company.
If they did have to move, then they would, and you'd have brain drain. But because they can remain in their communities (while earning the globally-competitive income that they would otherwise have to move for), they now pay taxes to their local government, buy from local businesses, mentor local youth, and so on. When they've earned enough money from their job, they may quit and start a startup in their own community, or become an angel investor supporting startups in their area, rather than yet another bay-area based fund. These are all good things!
However, if I was earning an order of magnitude more money than I currently am, I might want to pay a little extra to go to the really good barber, or to eat at the really nice restaurant at the riverbank. Or, hell, I might just employ a cleaning service every week, to save myself a few hours' time vacuuming my apartment. These necessarily local services will also see their revenues rise. To me that seems to be a more important effect on the local economy at large.
A healthy growth economy can tolerate income differences. But the balance is certainly precarious, as the example of New York or London shows. It’s constantly on the edge of driving out the remaining barbers and chefs because they can’t afford rents.