As far as I can tell timestamps have pretty much never come up officially in the US federal court system. But that doesn't mean they're worthless. Quite the contrary! It probably means they're so strong that no-one has been foolish enough to contest one in court rather than just settling.
Discussion
Re: usage, people are likely making something like 1 to 10 timestamps per second average with OpenTimestamps. I can't tell for sure though, as people making large numbers of timestamps per second can (and should!) aggregate their timestamps with merkle trees on their end.