There is no way in the current universe their transaction costs are <2% of a "big bank", as the advert above suggests (R112 in fees, vs R8936 at another bank). Sure big banks have vast infrastructure costs, but their cost per transaction is surprisingly low, from economies of scale ... much like a baseload power station has huge plant costs (capex and operational), etc, but their cost per kWh generated is lower than almost every other generator, especially small ones.
I know nothing about Bank Zero's service and responsiveness, nor their Ts&Cs. But I do know something about bank transaction costs, esp when it comes to IT infrastructure.
They seem to be appealing to that segment of the market that is very sensitive to bank fees, and that's quite legitimate of course. But they can't get away with pretending their operations are so efficient that they can cut fees to a tiny fraction of others. All else being equal (eg capitalisation, deposit management, statutory balance sheet cover, etc) if a bank is to survive it must make a reasonable margin. I hope Bank Zero is doing so, but they obviously aren't making money on fees so they must be making it elsewhere, and that can only be on playing customer deposits in various markets. All banks do that, but if you have less revenue from fees then you need to make that up from profits earned elsewhere, and those options are very limited, and that necessarily mean less distributed to their depositors/customers than would otherwise be the case.