FWIW... Churchill was primarily concerned with retaining colonies and keeping the Empire in tact... that meant keeping India...which the Brits lost anyway.
All the allied powers had an agenda of their own and real limitations on resources.
But I do think that a wide and dramatic campaign to make the information public would have been a positive element in promoting victory for the allies.
Actually the Brits basically ended their age of Empires when they signed the Atlantic Charter in 41 with the US.. FDR made sure that the recognition of self determination was part of the agreement, once this was signed, UK had no way it could hold onto its former colonies...
This act, requiring UK to recognize Self Determination of her subjects was the single biggest political act that ended the age of empires... it is given far less credit than it deserves.
No it didn’t happen overnight, but once they formally had agreed to it, there was nothing they could do to keep their empire in tact. The Age of Empires effectively ended the day Churchill signed the Atlantic Charter.
Possibly. But don’t forget a big part of the Final Solution was getting labor from the inmates to replace the manpower taken by the German military. Many of those who died were killed by a deliberate combination of starvation & overwork.