I've purchased a car privately this way.
Although, very sensibly, the seller met us at his bank and paid the Cheque in to his account whilst we were there. Fake Bank Cheques are a thing.
I havent used a Cheque Book since the late 1990s. We used to order take-away food in London and then pay with a Cheque and Cheque Guarantee Card when the driver got to the door!
Which of course meant you could buy food on a Friday if you had no money and didnt get paid until Monday! LOL :-)
The original BNPL Scheme! ;-)
But yes, I dont think they issue Cheque Books here in AU anymore. And if they did, what would you even do with one!
Can you imagine trying to pay in a shop with one!