There are still bills I pay with paper. (Some companies still charge for the "privilege" of paying online, which pisses me off even though the amount doesn't matter.)
I occasionally deposit checks via mail. Even if I trusted my phone enough to put banking software on it (which would be a silly thing to do), that only works for some kinds of checks.
Some companies respond to customer complaints via paper mail much better than they do via the net.
Sometimes I send checks to family members who aren't technologically sophisticated enough for there to be another way.
Maybe all of those reasons will disappear eventually, but I doubt that will be in my lifetime. It's also worth remembering that you can still send some mail anonymously - frankly, I'm surprised you still can, as there's nothing a totalitarian state hates more than anonymous communication.
For Canadians, cheques by residents are so passé. Businesses, of course, use cheques as proof of payment.
If you are doing consumer banking and If you do not take a special type of bank account, you are entitled to 3 cheques per month, and then whamo, around $7.00ea for the excess. So, we consumers have automated payment from accounts, or even online bill-payment options.
So, keep a balance to cover the cheques, earn no interest, and pay to make payments.