My electricity bill is around $180/month which in my eyes is a bit much.
Depends on the age of the house and boiler/furnace.
The house is built in 2010 or newer, then the house is in good condition because the house is filled up with good insulation system.. such as spray foam, proper rated insulation, vapor barrier, etc. No leaks anywhere.
You will check the boiler/furnace and see if it is either old or new... and whether it is energy efficient or not. Some old houses have leak... Contact your A/C specialist or contractor and they will scan your walls and duct to see if there is any leak.
The house that was built in many years ago... that didn't properly sealed like the new houses do. Sometimes people got their old house remodeled that is up to code and up to date which help them to save money for AC/heating.
Lastly, make sure the windows are up to the code ... such as double or triple panes windows are better. Not the single pane ones.
So, how can this device learn a schedule? I currently have a Nexia system, which I think is pointless to be paying $10/month to control it with my phone. Basically, I have a schedule made to let the house go to 75 degree's from 2am-6am, then 73 degree's from 6am to 8am, then 75 degree's from 8am-4pm, then go down to 73 degree's from 4pm-2am,
Nest thermostat is acting like a computer... it can save your programming for daily use .. so it can remember to start or change for you.... and you can even control it from your mobile device without getting up to walk to the thermostat.
I have one here but not same brand like yours. But I don't have anything to control it from the mobile devices.... I have to go to the thermostat to change manually when needed but it can change up or down in timely manner like yours.
Edit: I added quotes.