Generally they're unwilling to do that because it involves losing money for them.
Transfers work in a multi-step process to ensure money isn't created.
You tell Bank A to transfer money to person X at Bank B.
Bank A tells an intermediary bank C to move funds from Bank A's account to Bank B's account. (This step is unnecessary if either A or B are large enough to be an intermediary)
Bank C lets Bank B know that it's gained funds
Bank B moves funds internally from Bank C to customer X.
If you want your money back and Bank C says it's already been withdrawn then somebody in A,B,C is going to take a loss. Personally I think we should have an easy way to pay in a 7d settlement or something. Who really cares if somebody sends a 7d settlement when buying a house as long as its done 7d before closing.