Especially when you consider that it was coined to refer to literally impossible action. It's not meant to be about self-reliance or whatever, it's something that cannot be done.
THIS! A million times this!! It's literally implying the opposite of their intent in that you have to have someone else HELP YOU because you OBVIOUSLY can't pull yourself up by your own bootstraps!
One way to use this phrase correctly would be "No one can pull themselves up by their own bootstraps, we all need some help along the way."!