Hear, hear, David, and well said. Once the doorbell with hardwiring is installed, all you normally have to do is replace the doorbell button about every 15 years--and that's with a lot of kids visiting your house. I guess that a transformer could burn out, but I can't imagine what would cause that, other than perhaps a stuck button.
One thing that I have seen is that there might be a button by a rarely used door and that button can short from water or the button gets painted over, someone pushes it and it sticks. Both of these situations can cause the same problem.
The one remaining thing that happens is that someone, either a pro or amateur home improvement person, drives a nail through the bell wires. If you have been doing DIY projects and your doorbell quits while or soon after your project, the realistic thing is to think about something that you might have done to cause it to happen. And I'll bet that most of us, me included, probably would not remember the bell button or wires when tightening or replacing door hinge screws or even at the time of replacing a whole door.
And the best thing about hardwired doorbells is that you NEVER have to remember to replace the batteries. I have enough trouble climbing up, and remembering to do it, for the smoke detector batteries.