I've had a couple of reports that this applied to. It's incredibly disruptive. "I've got to fly back to India to renew my visa." "Okay, when will you be back?" "I have no idea, it depends when I can get an appointment. It could be next week, it might be in a month." "[State department] We're pausing all visa appointments." "Well fuck."
Meanwhile I've got a tech lead who is 12 hours away from the rest of the team. He was at least willing to work US-East hours while in India (basically staying up all night and sleeping during the day), but there was a huge amount of management overhead and inconvenience for the employee involved.
At least the procedure used to be that one would try to get an appointment at the US consulate in one's home country and then arrange the trip around it. Also, at least in my experience (but importantly, not with this administration) was that one was never required to leave the US.
The main constraint is re-entry into the US and being able to travel outside the US. If one stayed here, there was no problem switching schools, programs, jobs, adjusting status to permanent residency or naturalization. On the other hand, for re-entry, one needs a valid visa stamped on a passport which necessitated a trip to one's home country. This stamping visit could be unpredictable.
Ideally, one would like to travel freely to see family and friends but I see a lot of comments implying that one is forced to leave. It might be true now but a lot of comments here are conflating several issues together.
Props to your coworker. In my office, they usually just work normal India hours and we have a 12+ hour delay for all communications.
Honestly, this is kind of the point. Making foreign labor so unbearably difficult to work with will force companies to hire domestically. At least, hire more domestic workers than they would have otherwise.
I've worked at companies where we transfer people to Canada during periods like this in the same time zone. Sometimes they enjoy it so much they don't want to transfer back to the US.