If I have to pay, then why shouldn't I adopt a RFC 3161 or X9.95 timestamp service? Some jurisdictions recognize them as notary-equivalent certified timestamps. https://en.wikipedia.org/wiki/Trusted_timestamping
If what you want is legal protection then indeed there is no reason. Signatures vended by timestamping authorities are good enough for all uses I can think of unless you absolutely need decentralisation, in which case paying $10 to this company defeats the point. To get this service for free, just print your document to PDF, grab the free Adobe Reader, go to settings, signatures, click "Configure timestamping", then…
The technology used by such an authority would be just as complicated and difficult to explain as the blockchain approach to timestamping. What you're counting on is that the judge would give more weight to legal representations made by an otherwise unverified "neutral" private entity than she would to a detailed explanation of the blockchain.
What is it that explains how the blockchain--which doesn't require trust--would loose out to a private entity simply because bitcoin tech is complicated, and because a representative of that time-stamping authority would be able to sit in court and say "trust us, we have no stake in the outcome of this decision"?
A lack of trust is supposed to be the primary benefit of the block chain, but it seems that in your view in this case it is more of a liability.