The fact that your wife is already plugged into the Nest marketing hype says quite a bit. I wonder how much of it is "let's switch all the nest stuff over to Google phones." rather than a quest for technical know-how. The concept is pretty simple. This is a marketing decision...
Three billion does seem a lot for what must be the meager earnings of Nest right now. But Google is speculating that Nest has a much brighter future ahead of them. And they may be correct, especially if they can leverage Google resources into future products. Nest will need to produce Android apps for their thermostats as well as ios :-)
In 2012 I was at a company doing IoT. They have downsized a lot since. We had the phone app controlled thermostat, outlets, and power monitoring in devices.
The Nest seemed like a prettier version of our products. Ours looked like a thermostat.
This sounds more like a "who you know" than "what you do" aquisition. Nest was privately held so no numbers are available. The founders are from Apple and Google, so they had the inside track. Maybe Google is blocking Apple or Cisco?
Kudo's to the founders for a nice exit. We are just jelous because we did not think of it first, or did and could not get the fat payoff.