Earlier CQ used to run presubmit on the CQ host. This was unsafe, which is why we moved all presubmits to the Buildbot. Retrieving this information, however, would require talking to Buildbot master directly (to get the logs). Not sure if this is a good idea, but it's certainly doable.

From UX PoV, I agree.
Now, given current CQ design, CQ has no idea about OWNERS files. CQ sees this is a failure of a presubmit builder, and has no visibility in the actual failure reason.

There is a hacky solution polling for buildbot/LogDog logs of presubmit builder, and then parsing them for OWNERS check failure. But, as one of the owners of CQ code, I would vote against this approach on cost-benefit basis.

Another solution is splitting owners check into another builder whose name would be owners_lgtm_presubmit, and hence suggest easy fix.

Or we can change interface of CQ <-> buildbucket <-> recipe run so that CQ gets aware of the cause of failure, though CQ code would still be hacky.

I wonder if it could fall into Tricorder sort of things?

Quite possibly actually just so as to make them visible. Or a Gerrit plugin once we move it all to Gerrit.

There is no Gerrit OWNERS plugin which can provide the requested information about missing approvals directly in Gerrit UI. I'm not sure, however, if this plugin works with PolyGerrit UI.