changing history once public

I think I understand the issue with changing history on branches that
have been made public.

What is the negative of publishing a branch and not being able to apply
history changing commands?

If I want to keep this branch current (in public), I would pull from the
tracking branch resolve conflicts and push to my public repo.  This
action leaves my commit as the parent of another commit; it is not
longer at HEAD.  Does it matter if my commit is no longer HEAD of my
branch?

I think the downside of not keeping my branch current is that I'd be
handing off to my colleagues the task of resolving merge conflicts.  Is
that right?

Thanks,
John