I used to set my old programmable thermostat to turn on the heat an hour before I wake up and sometimes the house was too cold, the Ecobee turns on the heat somewhere between 30 and 90 minutes before I wake up to get the temperature up at the right time. Not sure if it uses weather data or just looks at how cold the house is to make that decision, but it does a good job.

The internet connectivity is useful for me since I'm away from home a lot, so I like the ability to get low temperature alerts as well as the ability to turn on vacation mode remotely or adjust the temperature (so if the forecast is going to be below 0F, I can turn up the heat from the normal 50 vacation temp to 60 to make frozen pipes in exterior walls less likely). If you don't care about that, then yeah, the internet access is not really necessary.

Similarly, the City of Austin has an energy savings program in summer where on hot days they will (with your consent) remotely turn up all connected smart A/Cs by a few degrees, which drastically reduces strain on the electric grid. I think I got $75 when I joined. And it can be overridden, so overall it has been a great boon.