The end of the accounting search

Because bouncing the cheque is the only option the bank has to move risk around - by bouncing a cheque, all the risk is moved to the payee, who can either chase the payer for new payment (using the bounced cheque as evidence that you owe them money), or discover that the payer is no longer in reach of English law, and that they've lost their money.

In contrast, with a system where the payer engages in a dialogue with their bank to ask them to issue a payment, the bank can move risk around to the payer, not just to the payee, by asking the payer steadily more probing questions until the bank is convinced that the total risk to the bank is low enough.

And remember that there's not just fraud risk involved - there's also the risk of someone writing more cheques than they have money to cover, leaving the bank with a bad debt, and there's the risk of having to actually offer some form of customer service to a customer who's been upset by the experience. By having the payer engage in a dialogue with their bank, which ends with either payment made, or payer terminating the dialogue, the bank only ever has to handle the risk its own customer represents; with a cheque written by the payer, the payer's bank also has to handle the risk the payee represents if the cheque is bounced, and has additional risk from the payer being upset because they thought the payment had cleared out of their account, and now cannot afford to pay the money they owe.

Fundamentally, the bank's goal is to reduce fraud risk to a level where it will eat the cost of fraud, and to reduce the other risks to zero because the bank would prefer to not spend any money at all on customer service (as is reflected in the quality of CS you get from a UK bank nowadays). Cheques are not compatible with this, since when things go wrong, the payer's bank has to supply CS to both the payer and payee, and has to handle fraud by the payee, while the payee's bank has to supply CS to the payee, and has to handle fraud by the payer. Internet banking works well for this, since when things go wrong, the payee is not dealing with the banks at all, and all the risk is borne by the payer's bank, who has to provide CS to the payer, and who can reduce the fraud risk to whatever level it's happy to accept.