I've not flown into Schengen airports recently other than Helsinki, but for that to work there would need to be a complete separation of transiting UK and USA origin passengers from all other international arrivals, (so the US / USA passengers are in the sterile channel from the point of disembarkation) from the disembarking gate to the post security checkpoint where the UK and USA origin passengers would presumably be invited to ignore security before entering a common sterile departure area.

But even then, the US government requires all interlining/connecting passengers to have had their hand baggage screened at their last airport before arrival in the USA, meaning that someone arriving from the UK may be "clean" as far as the interlining/connecting airport is concerned, but no so far as the final destination is concerned.