It really depends on how much close real-time collaboration is actually needed in your job. For some jobs/companies that may be high, for others where the work is done more independently, that may not be an issue.
I've done a fair bit of remote contracting from Asia working with team members in the U.S. and Europe and haven't had many issues since we're mostly working independently. Actually I'm currently in Japan/Korea working with NYC - probably the most inconvenient timezone difference (9am-5pm EST -> 10pm-6am Korea), but for my current project it's not really that bad since we're mostly independent and I'm a night owl anyways (also we have developers in Europe and India where the time difference isn't as drastic).
I'm not claiming that timezone is completely irrelevant because it does make a difference, but I think the bigger factor is the individual. I've had more difficulty getting in touch with team members in the same timezone than other team members in opposite timezones. In my experience, corporate culture overvalues the importance of being immediately available (not surprising given their open embrace of open offices and reluctance to adopting remote work) and underestimates the disruption and the productivity of deep, focused, uninterrupted work (eg. see Cal Newport).
We all have our individual work preferences. Regardless of what anyone's individual preferences are, I hope we see a trend towards greater freedom of choice in enabling workers to work how they are most comfortable.