Also, these services are usually reasonably priced, and sometimes even free, so it would be reasonable to use even if you're making several videos a day.
The immediate issue I see here is timestamping other people’s videos who produced them in the past, or for a different service, or just plain old didn’t know they needed to timestamp their video to protect it.
At the least, it's very, very strong evidence for a trial. Along with also emailing your lawyer or notary public a copy of the timestamp as soon as you create it, these factors would be virtually unassailable in a court of law.
I think the real problem is that evaluating such proof would need to be done by a human, and YouTube want a completely automated system.
Just needs a nice UI, and, well, Google giving a damn about it.