Courts are generally more tech savvy than techies like to give them credit for. But it's worth mentioning that in recent years several US states have already passed legislation expressly forbidding courts from denying such evidence (even/especially if put on Blockchains rather than a more traditional non-decentralized network/database), and you can find similar stuff in other countries around the world (even China). And of course in lower courts (like small claims) or even mediation the standards are a lot looser, there's not even a jury.

If you want a more thorough view of the rules in the US (which states deviate from to some extent), you might like to browse https://www.law.cornell.edu/rules/fre