Yeah, if you edit the log you could make a new chain when you fully control the chain. And if you send the log to someone else, they can hash it themselves to see if you tamper with it later. I don't get it too. What is the chain good for?
But if you're incentivized to publish as quickly as possible, then your customer gets the log immediately, and there is no need for a "trusted" third party to act as a "witness" and seek rents for not doing anything useful.
And none of the above protects against the vendor using your sensitive data to (a) do the work as contracted, with a cryptographically verified log and everything, but also (b) copy/analyze/abuse said data without telling you.
It's 2017 again, and someone on HN is inventing "blockchain for X", poorly. (Also note that it doesn't matter what kind of work X is, except for aligning this with HN's current main interest.)
Regarding incentives, this only works if the customer (or regulation) demands it - they’ll require the checkpoints as a condition of closing the deal - and is part of the bet.
A missed checkpoint is in and of itself visible, so if the vendor sits on records instead of publishing, the customer will notice the silence.