Isn't this just... normal? Maybe they use it more often, but (also in the Midwest as other comments mention) these uses are all more common than an actual apology.
But for a more distant example of the "I'm about to inconvenience you" usage being normal - isn't the Japanese "sumimasen" used almost exactly the same as these?
> Isn't this just... normal?
In the anglosphere maybe, but outside of that it seems to not be. My girlfriend is from SE Asia and her language's equivalent is evidently used exclusively to apologize for having wronged someone. I've had to explain my usage of "I'm sorry that [bad thing happened]" or "Sorry, but can I just [very minorly inconvenience you]" because she didn't understand what I was admitting fault for.
In her language I believe they use different politeness markers for these situations (they have an "excuse me" equivalent), but I'm not proficient enough to know them well.
As a learner it feels like Japanese is full of this kind of formalized, preemptory apologizing in all kinds of situations. You go to the supermarket and ask if they sell stamps (the answer is no) and they say the formal apology "申し訳ありません" (literally: I have no excuse).
There's also ごめん下さい "gomen kudasai" (literally "please forgive me") which is used as a greeting when visiting someone's house unexpectedly. And どうもすみません "domo sumimasen" (literally "thanks excuse me/I'm sorry") when accepting someone's offer to help with something.
None of these necessarily imply the speaker has actually done something wrong or wouldn't do the same again.