In my experience inter-continental flights to and from the U.K. are often a lot cheaper than from mainland Europe.

As an example, flying with Emirates to Dubai is often a few hundred euro cheaper from London that any other north and central European destinations they fly directly to.

Is that price without any connections? Because I suspect that flight gets most of its passengers from connections.

nor sure I understand the question. it's for a economy return flight (direct). funnily enough you can sometimes get a Lufthansa flight to Copenhagen for around 1000 and that connects through frankfurt. that's because copenhagen is more competitive from SFO. with carry-on that's a way to game the pricing but I heard they cancel the return if you don't check in in CPH.

Yes, that's what I meant (and you exemplified), they charge more for SFO-FRA than for a flight that has one of its legs as SFO-FRA

And I suspect most of the passengers on SFO-FRA are from European connections and don't have FRA as their final destination (or initial origin)

I just checked and you can get a flight with a 2 hour layover for $500. I'm not sure why anyone would pay 3x the price unless their company is covering the cost.