In every example I recall seeing where using an Oxford comma causes a problem it is because some sort of appositive or parenthetical phrase has been set off with commas.
Commas are the most common way to set off such phrases, but they are not the only way. Most grammarians seem to think that em dashes or parenthesis are acceptable, and I've seen styles guides that recommend doing that if there are commas in the sentence.
As far as I can tell if we just stopped using commas to set off such phrases when other commas are in the sentence (or just stopped using commas to set off such phrases all the time) that would get rid of all the cases where including the Oxford comma in a list makes the list ambiguous, without changing the cases where not having an Oxford comma is ambiguous.
Cue the em-dash, semicolon, colon, and parenthetical as secondary clause separators. If you still can't use the (in my opinion mandatory) serial comma without ambiguity then you need to rephrase.
This could be two people, but would normally be written with a different separator: "Betty, a maid; and a cook" (just removing the comma doesn't help because then Betty could be a maid and a cook). As-is, the implication is that this is three people. If you would like to make that more explicit, you would instead re-structure the sentence†, so it's not highly relevant to the serial-comma-vs-no issue.
†For example:
Betty, one maid, and one cook.
Betty, and a maid and a cook (a little awkward)
A maid, a cook, and Betty (depends on how you want Betty's inclusion to land for the reader)
Right, you can change punctuation to clarify it. However, it doesn't change the fact that the Oxford comma could make the list readable as a parenthetical phrase.
I'm not saying the Oxford comma is bad. I'm just saying that it isn't 100% perfect as many people imply.
I am begging you to accept the Oxford comma into your heart.