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That's pretty much what Gerrit does. Works with any git client, since it's just dealing with pushes, and can. E configured to merge automatically or with a manual nudge once the tests pass. And you can do this all through the command line; no GUI needed.

Comic author here. For the command-line I use a post-checkout hook to display the build status of a commit whenever I switch commits:

https://bitbucket.org/tpettersen/bitbucket-build-status-hook

That way if I update master before starting on a new feature, I get a notification if the tip of master is broken (or still building).

What would be nice is automatically attaching git-notes to commits indicating whether or not they passed CI. That said, I haven't looked into git-notes for a few years, so I'm not sure if they ever made it easy to sync them without a bunch of manual configuration.