Did Docusign really have a problem that couldn't be solved by any other means of publishing the hash?

Ultimately the hash comes from Docusign, so I'm not sure I can think of the problem case where someone doesn't trust Docusign to self publish that hash but does trust a hash that Docusign publishes to the blockchain.

Presumably, by publishing the hash on a public blockchain they are creating a trusted record of when the hash was published, which can be verified after the fact and which cannot be modified or removed, with planet-scale proof-of-work level of cryptographic assurance.

If they published the hashes on, say, their webpage or some third party's webpage, nothing would prevent them (or the third party) from redacting or removing the hash after the fact, given sufficient motivation.

RFC 3161 does the same, without a blockchain (public or private).

And how would you use RFC 3161 as a company that wants that use case?

I'd argue a more popular blockchain than their in-house one would provide stronger proof.

For example, a Bitcoin one: https://www.proofofexistence.com/

It looks like that is using 0.00025 BTC per transaction, which currently is $12 USD, that seems quite steep for a single document verification.

it is about timestamping basically nothing else. basically that cannot sign something in the past. Though you can do the same with sequence number, and publicly publishing all signed hashes.

Or cryptographically sign a statement with a timestamp.