Anyways. Here's my question: is this a good place for a house rule?
Yep, it's a perfectly good place for a house rule.
Should NPC hirelings/henchmen get three dying saves like PCs, or less? Should they die at one failed dying save? Or even dead at zero hit points? Or should they be treated exactly like PCs?
I'm afraid the answer really is "whatever you want".
I do kinda like the idea of using some sort of variant on "movie logic":
- Major NPCs, which mostly just means the BBEG and similar, apply the same rule as PCs - they get 3 strikes and then they're out.
- Lesser NPCs who remain important enough to have a name get either 1 or 2 strikes and then they're out. This reflects the movie convention that if a character has a name, they don't die off camera (the final Harry Potter film being a noted exception).
(Presumably, such characters who only have a first name would only get 1 strike while characters with a second name would get 2. As explained in "Galaxy Quest".)
- Minor NPCs, who don't even qualify for a name, die at 0 hit points.
Edit: Of course, another option is to not use death saves at all and instead give NPCs a flat chance of dying: 90% for no-names, 60% for one-names, 30% for two-names, and 10% for Major NPCs. But if the PCs bother to take an action to stabilise the character, thus investing resources to make that character 'important', then the percentage drops to 0%.