The reason why it isn’t badass is it prioritizies self over others

Did you not spot the “ethically and collectively” part? It’s very near the start of the comment and invalidates your entire objection.

In my view being “badass” is taking care of each other, even the supposed “least” amongst us

Couldn’t agree more if I tried. Except I’d change “even” to “especially”. Minimizing of pain, remember?

they often take on incredible personal pain to bring safety and security to others. That is what I would call badass.

Again, ethical and collective hedonism inevitably includes such sacrifice for the common good