Here's a scenario in urban areas where cheques are useful and perform a role that the retail payments system doesn't do.

Let's say you have a credit card issued by a Canadian FI.  Let's say in the case of this card, transactions are immediately reflected in both the "credit usage/availability" and the "balance owing" line items even though the transaction is not yet shown on the on-line "real-time" statement.   There's at least a two-day lag for transactions -- sometimes more.

Let's say, for argument's sake, you want to keep your "balance owing" to zero.  

In theory, you should be able to do that by making a transfer/payment from your account electronically to the card the same day as a transaction done on the card.   In practice, this doesn't work, because the payment lags.  The balance owing doesn't lag.

To address this, you can make the payment immediately by writing a cheque to the issuing bank, going to a branch of that bank, and depositing it the same day as the transaction.