Bloggs, I agree with your thought processes entirely, however you may be interested to know that the FCOM for at least one type (Avro RJ) recommends setting the missed approach altitude when conducting constant descent NPAs. The reason being, in part, that if the speed falls to Vmin and the speed protections kick in, the A/P automatically goes to Level Change. If a lower altitude is set in the window, the autothrottles retard and the aircraft dives whereas if a higher altitude is set, the autothrottles go to climb power and the aircraft climbs.
The downside is obvious, if you don't have the MDA set then you are in an unrestricted descent with only the pilots' awareness to keep it all safe. Normally that's good enough of course, but as in the UPS case, sometimes it's not.