Harlingen to El Paso

I was wondering:

If you filed GPS Direct Harlingen to El Paso you take a bite out of Mexico
around Big Bend, but gain 20-25 minutes no wind in the process. Wondering,
what, if any, problems are there in this sort of [depart US airport, land US
airport, but overfly Mexico during flight] IFR flight plan?
Will a direct clearance even be available? I would assume(?) no
customs/immigration needs upon arrival.
Perhaps people who regularly fly something like this route on the S/ SW tier
can tell what happens in the real world in such cases.
I'd also be interested of there's any difference between this on the
southern border, and, say a Detroit - Rochester NY flight overflying
Canadian airspace en route.
Thanks.