Other than one of the Nest models, are there any other WiFi doorbells which interface to a physical bell (as well as phones)? Obviously, there is the DIY option, but that is not what I'm asking about here (even if it might be reasonably trivial).
The Ring Pro is a hard wired doorbell, much like Nest's product. It retails for around $250. It also does 1080p video and has motion detection capabilities.
I assume you already have a hardwired doorbell, since you asked for that specifically, but if not and you are thinking of running wires, Ring also has the Elite line which uses power over ethernet. It retails for $500. The advantage here is that you don't have to worry about wireless coverage of your doorbell (at the price of double the cost) because it's plugged directly into your switch and providing power. Your switch does need to provide power over ethernet for this to work.
A word of warning, depending on your geographic location, such a doorbell may not be a great idea. The Ring products claim they only work between -5°F to 120°F (-20.5°C to 48.5°C) while the Nest products offer 5˚F to 104˚F(-15˚C to 40˚C). The low range may be a problem in the winter - and with the Nest there are some areas where the high is common multiple days in the summer.