Banks do sometimes verify funds manually, but keep in mind that verifying a balance still isn't a guarantee that a check will clear. The balance can change between the time of balance verification and check clearing.

What's needed to fully solve something like this is to put a block or reservation on a chunk of funds. So when bank A checks whether there's sufficient balance at bank B to clear a check, they'd need to put some kind of hold on those funds at bank B to have confidence that the check will clear. This is basically what credit card authorizations do, especially if the credit card is attached to a checking account.