Quite. And a cheque has a number so you can track things. If you give out the bank details you'll also need to give the person a reference code and hope they remember to use that with the transfer, so you can track it.
Also: what are the security issues with giving out such bank details? I know e.g. the Revenue does it, but do they have a way to prevent transfer out of that account except by some special arrangement? If I was TMH, I'd be wanting to have another account for the purpose, locked down so that the only way to transfer dosh from it was to some other nominated account. But I'd bet that sort of arrangement would also cost.