People tend to forget that you don't kill thousands people a day just by gathering the victims in some place and beat them to death or let them starve.

It takes a very strong industrial and logistical process to reach such yield, unless you commit very large numbers of personal to this task (for example the Rwanda genocide), and I don't mean white collar killers, I mean people who don't care ending their working day covered with blood and flesh of men, women and children.

In the case of the Auschwitz-Birkenau complex, the destruction of the gas chambers and railways would have stalled the process big time (for example, during my visit to Auschwitz, I learnt that the crematoriums were not even able to keep the pace with the gas chambers).

Of course, this would not have stopped the genocide, but the nazis would have had no way to murder people nearly as fast without the gas chambers.

I don't know if this is the result of a mild antisemitism or indifference on the US or UK side, I lack elements to answer such a serious and critical question.

But I know the allies were over-estimating the impact their bombings had onto the shortening of the war.

Maybe if they knew the truth about the moderate efficiency of their bombings on industrial or civil targets, they would have been less reluctant to divert some of their air power to take out death camps.

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Police cars carry three agents. The first one can read, the second one can write and the third one keeps watch on those dangerous intellectuals.
Unknown subversive activist - 20th century.