‘Let’ is not the right word. Let me clarify. My only source in this is my old copy of David McCullough's TRUMAN, FDR told Wallace that he was his choice for VP, but the choice at that time was not FDR's alone to make obviously. FDR could have put up a real fight for Wallace but was convinced by his advisors not to. But letting it be thrown entirely to the convention and not doing more than making a basic statement that he would vote for Wallace were he one of the delegates, FDR let Wallace be replaced by Truman.
Uh, you are totally missing the anti-Wallace movement by major democratic leaders. FDR was not convinced by his advisors. Wallace was defeated due to political maneuvering by major democrats at the convention.