Quite the opposite, governments and large companies even explicitly run services for digital timestamping of documents - if I wanted to potentially assert some

Quite the opposite, governments and large companies even explicitly run services for digital timestamping of documents - if I wanted to potentially assert some facts in court, I'd definitely prefer having that e-document with a timestamp notarized from my local government service instead of Bitcoin, because while the cryptography is the same, it would be much simpler from the practical legal perspective, requiring less time and effort and cost to get the court to accept that.