> What do you call an incomplete branch that is missing slices?

"incomplete", evidently. I don't see a real alternative here - you need some working space for an in-progress merge, and if you want to do the merge collaboratively, you'll want it on a branch. Just don't run CI on that branch till the merge is complete.

> Broken integration branches that leave a suboptimal history? What am I missing?

You appear to be missing the next step, where they use the merge resolutions from that suboptimal history to replay the original merge, giving you back nice clear history (and at this point, the integration branch can be discarded, presumably)