Keep the oversize tire and deflate it to clear the hitch.
The reason I need to always carry a spare in ALL my vehicles is not an old school thing. It's simply that almost every time I needed my spare was because the sidewall was destroyed. For regular flats, I always carry some sort of inflator and plugs. Most of the time. I never jacked a car up, just rolling the car to expose the puncture, inflating the tire and poking it with a rope plug. That'll get me home to where I could have a proper inside patch to the tire installed or replace it. In the old days, I would use the "Fix-A-Flat", but even though it now says it's compatible with TPM's, I wouldn't trust it. So, unless you want to be hanging out waiting for roadside and hoping they bring along a proper wheel/tire combo for your vehicle, keep the inflator, plug kit in your car and still carry a spare, deflating the oversize one to clear the trailer hitch. You can't fix a tire with plug or patch if the sidewall was damaged, despite YouTubes I've seen.
Not seeing a spare in a NEWER car is a cost cutting thing.