Time zones are still a thing. No matter how remote someone is, if they're more than a few times zones away it becomes problematic. More than nine timezones across the company is nearly impossible to do well.
So if we're talking about a US company, if you want anyone on the west coast, hiring continental Europeans will be tough, unless one of those groups is willing to work outside normal hours.
Also, taxes can be hard. I'm sure as remote working gets more popular, services will pop up to help with this and maybe laws will change, but right now, it's really hard to hire someone outside the US, and it's fairly complex to hire someone inside the US in state that you aren't already in.
The most likely outcome of remote work is a lowering of salaries in the big cities and a raising of salaries in more rural areas, as salaries tend towards the national median.