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.
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.