I transfer through Heathrow a few times a year, normally when doing an ex-EU. My big gripe is the variability of it. Sometimes the people working on security appear to be awake and helpful, then you get through quite quickly (passengers ignoring the quite clear instructions not withstanding). Other times, the security staff are glacial, everything backs up, they pull every second bag for secondary inspection then vanish, they're rude and unhelpful etc.

On a good day, I don't find it noticibly worse than transiting somewhere like Amsterdam. Different, sure, but not that much worse. On a bad day, you just want to scream...

They need to fix the staffing problems, then sort out the queueing systems which don't always work well (eg long empty tensa-barrier queues with staff who shout at you if you try to duck under / suggest they might want to open it up), then it wouldn't be too bad.

Assuming the USA has the most stringent screening in the world is just not true. They are average.

However the UK Department for Transport chooses not to allow any UK airport to allow unscreened passengers from anywhere else. This is unlike most of the rest of the countries in the EU which choose to allow unscreened passengers who have been screened in another country deemed to have sufficiently good screening (EU, Schengen airport, or USA).

With the current xenophobic tendency in UK government and general noisy chaos in UK politics, this is not going to change any time soon (years). All that can happen is that it is made more efficient, which may happen, if Heathrow Airport ever manage their staff properly and get to build larger facilities.

They pay the high Heathrow Passenger Service Charge.

That's the flaw in your reasoning. As has been proven over and over again, including the TSA's own tests, this is simply not so. The U.S. may have the most security theater and perhaps the most security hassle for travelers, but the most real security? Far from it.

Americans are not always objective about this, we want to feel good about what our country does, but the folks who run foreign airports generally are.

Because (1) there is no compelling reason Heathrow Airport would benefit from this, (2) passengers coming from US/Canada flights are not segregated from passengers coming from elsewhere, and it would be prohibitive to set up such segregation, and (3) Global Entry and Nexus are programs related to immigration and customs control.

Not quite true. It permits unscreened passengers from airports who adopt the same standards that they do. Which none do exactly, therefore it amounts to the same thing, but is a subtle difference.

At the risk of further splitting hairs, passengers screened in JER, which is not in the UK, may sometimes join a flight at a UK airport (namely LGW) without going through further screening.