Former speaker of the chancellor (and TV news anchor before that) is German ambassador to Israel. Next ambassador will be a career politician.
It‘s not uncommon, though I‘d say even the „cool posts“ like Paris or London usually go to career diplomats.
I know nothing about this but JumpCrisscross seems to use "political" to mean "has donated large sums of money" while your use of "political" is more like.. someone who does politics.