Even when the 'grand alliance', to borrow from Churchillian parlance, was in place, there was a significant level of mutual distrust between the Western allies and the Soviet Union.
Stalin wanted, indeed needed, aid and assistance from the West. However, he wanted this aid on Soviet terms. Having a significant foreign military force based in the Soviet union under separate control was running perilously close to the intervention into Russia in 1918/1919, seeking to restore the Tsarist regime.