There's usually stringent laws when it comes to hiring people (depending on where you are, I guess). The company I work for, for example, had to sponsor my work permit in the Netherlands for it to be legal to hire me, since I'm not a EU citizen. That's a stressful, expensive and time consuming process for everyone involved, and in general it's just easier for them to hire local talent since they don't have to bother with all the extra steps. I'm not sure of how that works exactly in the US, but I can't imagine it's any simpler or more convenient.
Now, companies might move onto hiring more freelancer type workers to circumvent these issues, but that also has its slew of problems. They're usually more expensive, you have to spend time and resources onboarding them onto the project, they have to get used to the project and its intricacies, they have to learn how the team works, the process for paying them might be different than your usual workflow, they tend to leave just as quickly as they came which compounds the other issues even more.
I think things will mostly progress as they always have. Sure, there will be more competition, but that doesn't necessarily mean that hiring non-local talent is the easiest way to go for most companies, plus as can be seen from any discussion about WFH on HN, there's a sizable group of people that don't enjoy WFH and would rather stay in offices anyways. The WFH crowd like me will be free to pursue a company that suits their needs, and the ones that enjoy WFO will still be able to choose those companies that prefer that. Win-win, in my eyes.