Sure, that would be fine. They could also use a totally wacky format, I don't care. The problem is that without a standard the JSON tools in different languages don't all agree on how to serialize dates and you end up needing to deserialize/serialize manually the smooth over the differences. The problem isn't that you can't represent dates; it's that there is no standard way to do it.
That's not "standard." That's one of many ways that people represent dates in JSON, because the JSON specification itself does not mandate that you use any particular representation. If you use it there is no guarantee it will be recognized as a date on the other end.
