Well, a lot of the factors explicitly have nothing to do with general productivity at all, such as alignment. The goal with regards to selecting for productivity would be "someone who seems productive enough" but getting hung up on exactly
how productive feels like a mistake, as aside from being unquantifiable, that isn't going to be the only or probably even main factor that decides the fate of the endeavor. Productivity is not the most challenging problem in software development. In my opinion, as far as factors for success for a technology endeavor goes, even overall technical competence winds up factoring in fairly low at the end of the day. What's important is meeting the threshold you need, not getting as high of a score as possible.
I should clarify that I actually agree with you if what you're saying is that the best measure of productivity we have is literally just going off your gut, but my argument is that this gut feeling is terrible. This is in large part because humans are biased, our gut feelings are swayed by things that simply shouldn't factor in. We tend to have more positive opinions of people that we think are like us and we sometimes wind up having negative opinions of someone based on stupid things like disagreeing with them on something that is ultimately irrelevant to whether or not they are productive.
And to me, the ultimate nail in the coffin is really in the question of what really constitutes productivity. Productivity is supposed to measure the efficiency of producing something, which already has pitfalls in and of itself when dealing with things that do have discrete, measurable indicators of progress, but programming doesn't, it's not even always obvious if progress is forward or backward sometimes. What's most important, performance optimizations, disaster planning, features, robustness, minimizing resource utilization? The best answer you can generally say is "It depends," and moreover, everyone will have a different set of competencies they're best at, so a person doesn't really have some single "productivity value" you could summarize them with. Yet, all of those things are pretty important for any serious technology organization, so you would want people with a variety of different affinities.
At that point, it starts to beg the question of whether or not attempting to directly measure software productivity is a worthwhile endeavor. I'd argue not.