Yes, you're correct. On the other hand, there are already numerous tested and proven workflows to implement both the bissectability and clean history, AND allow for the work-in-progress dirty history.
In the simpler one, you use at least two work branches, plus the mainline branches. You move the ready-and-tested work from the dirty work branch to the mainline through an intermediate cleanup branch. The no-mess, no-regression, clean history for bissectability requirements exist only in the mainline and intermediate cleanup branches.