The slighted musicians, as you put it, have made plenty of experience-based comments on what the drawbacks are, and why the decision matrix is wrong. They accord with my own (admittedly amateur) experiences. I think it is disingenuous to dismiss their comments with a casual "whether or not you think that's accurate" - that's exactly what their comments are, they're disagreeing with the decision matrix and giving their reasons why.

See especially the comments made by professional tuners (which matches what my own piano tuner tells me).

The people in this thread are nuts. I play music at a very high amateur level and know a lot of people with both absolute and perfect pitch. They all enjoy showing it off and are great sight-readers. It's a little more annoying for them to hear music at a less-than-professional level, but no more so than anyone who develops their ear to distinguish between subtleties in other parts of playing like phrasing or rhythm.

(Maybe that's less true for true perfect pitch, though.)

Relative pitched people will be able to easily match what the next pitch ought to be if you play the beginning of a song they know in a new key. Absolutely pitched people (in my experience, unless they've been trained) find this difficult.

Imagine if, someone showed you a two and you just saw in your head what 2 + 1, 2+2, 2+3, 2+4 were intuitively. This would give you a leg up in elementary math (And beyond). This is similar to what relative pitched people experience. An absolute pitched person often just sees the two and if they see a three, the relationship between the two has to be learned.