That depends heavily on where you live. If the most common type of power outage is one that affects a small region, it's quite likely internet connectivity could remain unaffected. I had this experience in northern Sweden, where I had a couple of power interruptions but zero network interruption.

I live in Oakland, CA. Internet is definitely more reliable than electricity. My smart home devices send me an email when there's a power outage.

Could that be coming from the smart home device manufacturer noticing the device was abruptly disconnected?

The device itself is a Nest Protect fire alarm connected to 120VAC. It has a built in battery back up.

It could be, but it is probably just they have enough backup power to send the signal.

It's more likely that the device sends a heartbeat every minute or so, either for notifications or just for this "device is offline" feature.

In this case, no.

Most people's home internet connection relies on electricity though. Internet will necessarily be less reliable than electricity for them.

I just hook up a UPS and the first thing that is on it is my router and my key devices.

It is not just about power outages, it is also about cloud services closing, having outages etc - as in this post. If you only have devices that will work locally, that becomes much less of a problem.

Eh. Depends on how mission critical it is. I don't mind an appliance needing the internet as long as I can still physically operate it during downtime.

We should all move our homes into the nearest data center. I call the locker next to the Layer 3 drop.