Many existing smart doorbells do actually use the existing wiring and chime of the doorbell. An example is the Google Nest Doorbell.
So in terms of "wasting what you already have" what you're wasting by going with a typical consumer product is basically a button that you can buy from Home Depot for $4.98.
Now, obviously, someone interested in this project is probably not interested in having a proprietary Google camera on their door. But in my experience most people who want their doorbell to be "smart" actually want it to be a security camera and a two-way communication device so you can relay information to the person who is ringing the doorbell. Otherwise, what good is it to know that someone rang your doorbell when there is no other information? That amount of information is just like a random timestamp, at that point I'd just keep my dumb doorbell.