My view on this is rather different, but mainly as the definitions I use seem to be different than yours.
The UX Hierarchy of need
- The set of tasks a user can perform on the system.
- Often referred to as utility.
- How stable and consistent in performance the system is.
- Bugs and downtime fall in here.
- The amount of effort that has to be expended in order to perform a task.
- Broken down to:
- Cognitive effort:
- Decision making (by the cognitive theories I believe in, decision making is not a separate process, but rather a high-level form of statistical resolution, which in evolved cases is highly conscious; but decision making has particular importance in UX so I include it here nevertheless).
- Physical effort (mouse travel distance, click count, etc. will fall here).
- The emotional, subconscious impression the system leaves on users.
- Although in the illustration affectivity is shown as the 4th step, in practice it is the outcome of all other three (and marketing), and thus is really a wrapper to these.
Given the definitions above, NPS, in my view at least, is clearly part of affectivity.
An important thing to mention is that if you ask "How likely is it that you'll recommend this product to a friend or colleague?" and then follow it by "why?", most people's answer will fall into retrospective reasoning rather than an active one. In other words, the decision has been made first, only then reasons are 'made up' - which further supports the idea that it is emotions that play a part here.
I don't think NPS is any indicator of functionality or usability (and definitely not reliability).