My employer did just this. Nothing crazy restrictive (or at least nothing unexpectedly so, given the nature of local taxation etc). IIRC, it's basically "if you're going to work somewhere for more than 2 weeks, you need approval from your management chain (who has to submit requests to HR/payroll)."

There was additional language about international travel. We have many Indian (and other immigrant) teammates living in the US who travel home for extended periods.

I did just shy of 2 weeks in Florida earlier this month, all that required was a heads-up to my direct manager, no approval required.