Not only do you have to connect your Davis Vantage Vue to WU, you need another piece of equipment to do that called a Meteobridge.
The Meteobridge polls the weather information on your Davis and formats it to what is required for services like PWS Weather, Weather Underground, Ambient Weather, and others, and then uploads the data to those sites.
The Meteobridge can use WiFi or wired Ethernet so you should at least be happy with that.
Don’t ask me why Davis cannot directly talk to WU.
I suspect Rachio could talk directly to Davis, after all the Meteobridge does. I suspect because there are so many different weather stations that Rachio would rather leave the job of interfacing to others and just have one interface to WU.
You can build your own if you are Linux savy or purchase one. I installed one some years ago and it has worked flawlessly.
For more details:
Regarding the Rachio WiFi interface, if you have a solid WiFi setup you should not have any problems. It is not glitchy and reconnects well after power failures, etc.