Unfortunately wisdom tooth removal is basically required for polar programs deployment, otherwise I'd surely still have mine

Same here. Not polar, but another similar program. But when the dentist went to take them out they were practically sideways in the worst way. My dentist, who also happened to be my father's first cousin, took one look at the x-rays and referred me to a maxillo-facial surgeon. I was scheduled for general anesthetic and the Doc had to chisel them out.

Not having them out could have easily become a life threatening situation in a real short order. So, if i hadn't been removing them to comply with those rules, the teeth themselves would have enforced a removal at some unplanned time and at potentially life threatening inconvenience.

So, you <might> still have yours, but I certainly wouldn't still have mine.

I had the same situation with the Peace Corps. No dentist ever wanted to take my wisdom teeth out, but the State Department had other opinions.

Even the oral surgeon seemed to only regretfully remove them when I handed over the forms.