If you believe they are neither vices as well, then I can see your point — they just are.

Perhaps this is the point you are making: if one is data-driven and engineering-oriented without regard to the consequences, that could be seen as a vice.

Despite the amazing engineering/science, it is hard to come to peace with von Braun or Teller (just to pick two examples).

Yes exactly. But until this is clear and accepted, these terms are apt to be misdirections—for example here, in a discussion trying to understand how things went so wrong at a leading tech company.

Hopefully we can get to the point of putting purpose (I think “mission” is a bit too hackneyed and neat to work here) first in discussions of culture, whether corporate or engineering culture.

I think most of us want to view "engineering culture" as just problem solving, amoral. If these companies we worked for didn't have such an outsized effect on the greater world we live in that would probably be a reasonable way to view engineering culture.