I've worked for companies as a remote worker, and I've owned a company that for its entire lifetime hired remote staff. In my experience, as long as you hire good people, the time zone delta is the only limitation that's extremely difficult if not impossible to overcome. Everything else can be solved with good communication (which should exist anyway), good requirements (which should exist anyway), and good process (which should exist anyway).

If the time zone range of a team is less than about 4, then in my experience the team works quite well. If the range is greater than 5, it almost always encounters problems that even good process, requirements, and communication struggle to solve.

There are always exceptions, of course.

This was my experience when I worked remotely for an East Coast company while based in SF. When I joined the company the expectation was that I would work Pacific hours, coming online around 9am PDT. Of course reality proved very different, and slowly my start time crept earlier and earlier until I found myself online at 6am daily - I was effectively working 3-4 hours longer than my East Coast colleagues simply because of the timezone I was located in. I didn't last long and moved to Bay Area company that allowed me to work from home 2-3 days a week.