You can still pay by direct credit to these companies though can't you? Some like mightyape uses ASB banks online eftpos as an option too, where it connects directly to the bank, rather than using a third party system. I am guessing that is safer, as I am guessing that is supported by the bank?
With AirNZ and Jetstar it's POLI or credit card (with surcharge) payments only.
Or use OneSmart with Air NZ and you pay no credit card fees.