Having private branches also does not always work. For example, there was a purge of unnecessary branches in our main repository. If I use a fork of main repository (and I do), my private branches are also not readily available to the team.
The choice is done for you. It is not yours or theirs often enough.
Personally, I think that the only bar that is necessary is that commit history should remain readable - which is subjective, but that's why we have code reviews. In any case, this is not an issue with the tool, but rather with the religion that formed around it, which is often the case with software tooling.
One thing that helps a lot with a pragmatic consensus is to ensure that all members of the team have personal experience debugging old code that they didn't write or previously review.
Either you can break your big commit down into pieces that can be applied one by one - then do that using history rewriting (and testing each part!).
Or that's not possible, e.g. because it's a global architecture change or something that is already atomar. Then there is nothing to bisect anyway - there is nothing that can be done, no matter which tool you use and no matter if you squash or not.