I'm not sure what kind of audience you think it works on.
I tend to get (particularly from people under 40) one of two inappropriate reactions to reflexive self deprecation - either exaggerated sympathy for my plight, or treating it as an exposed weakness to attack.
(Probably the questions aren't literally stupid, or the person maybe would never have been hired in the first place)
Sure...but I think that an insight that I've gained is that this is an example of a formula which doesn't really communicate or explain all the things you mention. You aren't sorry, you don't know that your question is basic, and you don't think you're wasting peoples' time.
In effect, it's a "pointer" to a bunch of things, so it only works with people that are conditioned to such things and have them in their memory. One of the things you mention, "not trying to school them" sounds to me like deference, and I don't think deference can be quickly established without a formula. Like a salute, you have to do something arbitrary in a mutually understood way.
Yes, some people will pity you, or treat it as a weakness. But having the courage to admit when you don't know something is a valuable trait that most people (in my experience) respect.
Also if you demonstrate your knowledge in other areas and contribute value to the meeting, people tend to forgive a few stupid questions in another area.
It's like when I'm having a meeting with my manager and I want to talk, so I start, they stop, I apologize for interrupting, and they say no, no, go on.
I assume there is no emotional drama going on. If they really want to continue talking, they can do so. That's why I apologize and pause. I'm not sorry, but I need to show appropriate deference.
It would be unfortunate if someone was building up resentment because they're not on the same wavelength about appropriate behavior. The purpose of etiquette seems to me to provide a formula to negotiate common situations without having to navigate emotional complexities.
But when different people have different rules, there's not much that can be resolved.
I’m reminded of Arthur Dent (British) in the Hitchhiker’s Guide telling Zaphod, modestly, “oh, it was nothing” about something great he did, and Zaphod responding along the lines of “oh, it was nothing? In that case forget it then”, which was not at all what Arthur intended.
But being self-deprecating was not one of them. I feel like I'm surrounded by Zaphods, or something, and I'm not sure when it happened.