The obvious answer is that if someone is a second/third/maybe choice and might be getting an offer later, no-notice is better from the school's perspective. Completely unclear to me though is why not to say "no" to a definite no. A second reason might be that it is uncomfortable to say no to someone (though I expect editors and seniors to be accustomed to that).
I want to make three points in support of (detailed) notices, and I am curious to hear other perspectives and comments:
1. Is the first point even true?
Candidates hear a lot of rumors and most likely know they weren't the first choice anyway. And I believe there is in general understanding of a match component, so I don't think people are offended if not first in line.
2. Information is helpful, from instrumental and mental perspectives:
From the candidates perspective, uncertainty is one of the most brutal things to deal with (see the recent mental health of candidates survey). If it's a no, rejection will have to be dealt with anyway. Providing information on objective chances can help in making peace with a rejection, or make an offer even more sweet. For departments this is one hire or another, but for us candidates is our foreseeable future. In many instances candidates have nothing else to do at the time, but sometimes there is -- and in these cases, think of us and the instrumental effects of information when we need to make decisions on other prospects.
3. Substantive feedback is extremely helpful:
Avoiding rejection notices, or updates, also takes away a candidate's opportunity to improve (and this is true also for AEA interviews). You, hiring departments, have a lot of power to provide valuable feedback that will be helpful -- in presenting one's research, interviewing in the future, framing agendas, etc.
What to do?
Think of it as editors -- you send a letter explaining why you made your decision, and you try to make it clear it is about the paper and not the researchers, right? You wouldn't imagine "never notify a rejected paper" as a good mechanism, would you? This case is not too different.
After making decisions, provide all invited candidates with information about the process. Send messages to these few people making it clear that this is not a rejection of the candidate as a person, and not even as a researcher, but is due to other reasons -- and say what these are. Say, for example, "we are in higher need of someone who can teach econometrics, but we might call you if these candidates will not accept our offer", or "your presentation was clear, but we were not sure you addressed external validity concerns in your research and some members of faculty found it to be disqualifying".
I will be happy to hear the thoughts of senior, junior, recently hired, and my fellow candidates!