In particular they tend to be used for small businesses, associations and the like because they won't have proper accounting systems set up to track transactions. The cheque stubs form a useful source document for book keepers, accountants and auditors.

Also, a chequeing account can have a requirement for multiple signatures. This matters a lot for partnership-style businesses and of course incorporated and unincorporated associations. Indeed most model constitutions for incorporated associations specifically mention the chequebook, who possesses it and who must sign cheques.

Even so, it's dying out there too. Bank statements have gotten progressively more descriptive as time goes on. Plus the banks are grasping thieving mongrels who use "but it's paper" as an excuse to slug you for stunning fees for every node in the state chart of cheque deposits.

I have cheque books and deposit books for my Pty Ltd accounts and I have never had occasion to use them. I pay bills with the corporate credit card and since I deal with large creditors they prefer to convenience and reliability of direct deposits.

I suspect that it was a bait and switch attempt to phase out branch banking. I.e. make it free until everyone switches over then start charging fees. But it backfired.