Whatever role FDR and other Americans played in the demise of empires IMHO it was to act as a catalyst, aided by a refusal to provide support for a revival after victory. The empires were exhausted by WW2, their national focus had always been on "home affairs", the colonies had a mixed profit/loss record and there was a massive loss of confidence. FDR just speeded things up, although it took sometime for the colonies to be disposed of.

India for the UK was 'the jewel in the crown' and after 1947 colonial policy was missed its central hub.

Nor must we be too UK-centric, others had colonies, notably France and the Netherlands. Portugal took longer - 1974 marking the end.

When I say 'other Americans' my recollection is limited. Were there not Americans in a variety of roles around the empires "doing their bit"? I recall there was an OSS mission with the Viet Minh in French Indo-China (in North Vietnam) and did they not advocate a handover to Ho Chi Minh?

I wonder what was the impact of seeing French colonial administration in North Africa? After Operation Torch the French remained in power and the USA used the area as a base for the Italian / South France campaign.