Common presentation of time doesn't really help if the datum isn't set in some way. I can present today as 1448/03/23 since today is 22 Rabi' al-Awwal 1448 AH. The presentation of YYYY/MM/DD is kept standard, but it uses a different calendar with a different year zero and a different year length.
If two places can't standardize time, why should they strive to present it uniformly? Also, it makes recording how time is kept important to the time's recording as you've now brought in the wrinkle of how to handle relativistic time.