Western Allies (USA, England, Canada, France, Dutch) bombing Auschwitz was not a mission that had a necessary probability of success.
Blaming FDR, does not obtain.
Stalin and Russian forces were much closer.
First western allies aerial recon flight over Auschwitz, occurred on April 4, 1944.
May 1944:
60th Photo-Reconnaissance Squadron of the South African Air Force operating from southern Italy on 31 May 1944
https://www.yadvashem.org/from-our-collections/auschwitz-aerial-photos.html
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Forty-six Douglas A-20J and A-20Ks were modified to as “F-3A” night reconnaissance machines with a K-19B camera, four flash bombs, and with the ventral tunnel gun deleted:
https://www.airvectors.net/ava20.html
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Russian military [U.S. built] Douglas A-20’s would be the most abundant and closest bombers capable. Examples:
https://www.worldwarphotos.info/gallery/usa/aircrafts-2-3/a-20/