Oh, what's wrong with inattentiveness? I guess your main claim for the virtues of the trait lie in the presumption that an inattentive person is doing "something else" of value. I'm saying it generally isn't so.
The kind of inattentiveness I'm writing of gives person bad school performance, makes them appear lazy in the eyes of an employer, makes them seem unresponsive in the presence of a company, etc. Now that's their choice to do them, and it's everyone else's choice to deal with it as they please.
I'm in for daydreaming, silent thinking and all that, but this kind of thing is just less, not more. Of course, it's OK for anyone to settle for less, and inattentive people do just that. The problem comes if there's a mutual project that requires roughly equal share of the activity for all the people. The solution is then not to include the inattentive person in the activity. This is also fine.
Now my wife is pondering if she's eating well. Perhaps she's tired because of not meeting the daily nutritional requirements. The thing is, it's not just me telling her what to do or some crap you'd expect of ENTJ. She's missing out from a lot of things because of her inability to keep up. She compensates by going into situations that don't require her to be fast. That's fine as well, I just can't figure out why a person would cripple themselves that much voluntarily.
Okay, I can figure out some relative merits of inattentiveness. The relative independence from outside events gives a person some calmness. Not everyone is of the type who's the first to react to sudden events, nor do they have to. I don't think my wife's traits are worthless or anything like that. What I'm saying is that rewards from the "outside world" are commensurate with the investment made, and inattentive people don't invest much.