I can't get by without a chequebook but that's no slight on me - but the people I am dealing with who seem to expect you to be able to write one.
Lots of tradesman I deal with dont even know what an online payment is! They certainly would have to specifically dig out their bank details which of course they could but they dont know them off the top of their head. They dont appear on their invoices.
Its also awkward - a tradesman who has finished a job and wants paying, either has to leave the premises without being paid and hope you do an electronic payment fairly soon, or hover over you whilst you do it there and then! Whereas a cheque is being paid, he can leave the premises. Okay, so he might end up with a bad debt anyway if your cheque bounces, but at least a transaction of sorts has taken place.
You're right, its handy also for all those school and preschool bits and bobs. Cash is all very well but they seldom supply you with a receipt at the time, and they never have change and its always some silly little amount.
Paying bills I generally do electronically or by direct debit but there is the odd random one where it takes a lot more time and effort doing an electronic payment than scibbling out a cheque and chucking it in the post.
I agree however that paying at the supermarket with one, only to then get your chip and pin debit card out to guarantee it, is ridiculous and should be scrapped! (and has)