Of course cheques cost money. Getting rid of them allows banks to slash costs which will not be passed on to customers. ASB a few years ago stopped accepting cash via the Fast Deposit boxes, then months later removed the service altogether. Given cheques are still handled by the branches, along with other tactics such as automatically opting people out of paper statements and charging $0.20 for a verification text that costs a fraction of that, it's clear these changes are driven by profit, not practicality.
There is currently no substitute for cheques, especially for large purchases and business transactions. Even if the bank's savings were passed on to customers, the additional staffing cost to businesses, having to login to Internet banking to perform comparatively time-consuming one-off transactions, or waiting in line for manual transactions or to use ATMs, or making phone calls or visiting the bank to approve a transaction above whatever the bank arbitrarily decides is an acceptable limit, far exceeds those costs.
If you're happy to pay fees for alternative payment methods, go ahead.
It takes a couple of seconds to login to IB and set-up a payment.