There are no "take-home" tests with "results in minutes" that use PCR technology.
I was in London and Belfast last week between December 24th and January 1st, travelling from the U.S. (SFO airport)
I had to take a PCR test within 48 hours of boarding, and I had to take a PCR test upon landing in London, and was asked not to leave my hotel room until the results came back -- nearly two days later. They checked my vaccination and PCR test result before I boarded the plane, and passport control at the airport asked to see confirmation that I had a PCR test scheduled.
Before returning from the U.K. to the U.S. I was allowed to take a "rapid" test, but it had to be supervised either in-person or with a "tele-medicine" service that watches you over a video camera.
If I had tested positive, I'd be required to quarantine for 10 days in the U.K.
There was no requirement to test after landing, but I did--three times. NHS gave out rapid tests in "7-packs" and I was able to get 4 packs.
Preparation is a thing. It was quite obvious we were likely to have a covid spike this winter. Anyone without a stock of antigen tests at this point has simply been irresponsible as it was trivial to buy a few boxes at $14/ea at walmart the past 6mo.
Abbott both destroyed unsold inventory (6-7mo from expiration dates) and closed down one of their production facilities they stood up for these tests due to lack of demand over the summer.
If everyone was a "prepper" (no, I don't think having some basic $7 tests sitting in your medicine closet really reaches this point at all, this is called "being prepared" and used to be a civic duty taught to children) the production would not have stopped, and they would not have let 2500+ workers go they are now scrambling to get back.
tldr; production was there, it was ended due to lack of demand. Yes, some (many) folks are in a financial position where $14 is a large expense, but those are outliers and certainly not the folks asking if I have any tests on hand right now.
Not sure if there are proctored PCR versions. They'd have to go in the mail to a lab, but the test proctor could watch you seal it with a uniquely marked seal or something; that should ensure the sample that arrives at the lab is the same as the one you swabbed on camera.