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.
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.
Usually, private branches are get deleted after merge happen.
In the end, I will have a situation where there is a defect in the main branch and there is no way to bisect it narrower than to squashed commit.
What should I do with 3200 changed lines in 320 files when there is a defect?
[1] https://stackoverflow.com/questions/4049958/embedded-softwar...
The page above hints that pre-review defect density for C/C++ code is 4.5 defects per 100 lines of code. After review it is 0.82 defects per 100 LOC, or 8.2 defects per 1000 lines of code. My big patch will introduce 25 defects that'll pass review. Even 10 fold decrease in defect density after testing (haha) will not significantly reduce probability of the introduction of a single defect.