I fully understand the premise. And yes, the case I presented: "rent is an estimate of the value of a property to be used for a specific period of time" is technically a form of a partial interest. A more common form of partial interest, however, is when there is more than one owner of a property, and an appraiser is asked to estimate the MV of that interest, which is generally not associated with some interim time period. Again - as I said, I get the thought process, I just disagree that estimating rent is an appraisal. And again - that's just me. I'm not here to convince anyone to come around to my crazy ideas.
Well, first of all, a borrower isn't going to determine a purchase decision based on the rent estimate without some method of associating that rent to an overall value right? IOW - even if not explicitly developing a GRM (or cap rate), in their mind, they're using some tool to associate that rent with a purchase price (or value).
Of course others can quantify that - but in your scenario, the appraiser isn't.