I have a little concern about why the WH or DoD said that one of the pilots was recovered during the initial hours after the aircraft was lost.
Surely then when they let slip that it was an F15, the Iranians knew full well that it is two crew.
So they would have gone into overdrive looking for the second crew member.
Surely there should be ongoing silence from the US and Israelis as to what is happening in the war, only releasing a careful narrative with say a 2 day delay.
The continuous nonsense from Trump, WH briefings etc are keeping the markets and the oil price in a spin.
While the OPSEC on the second crew member nearly cost him his life.
FWIW could us Brits have carried out a rescue. Probably but it wouldn't have been quite so stunning.
It would likely have involved 4 Operators in a taxi with a local guide, a lot of tea, a great deal of walking and some backhanders to some local dignitary.