One would think that a new homeowner, if actually locked out of the thermostat somehow, could go to their local hardware store and pick up a cheap $30 thermostat to control the furnace.

Or just remove the thermostat from the wall, and turn the heating on by shorting the signal wires together.

Yes, or that. Point is, the only thing that’s locked/secured is easily removed and replaced by a dumb, easily acquired device. Nobody that has accepted the responsibility of home ownership will be denied access to heat due to a smart home thermostat that they don’t have full access to.

After I bought a house, I couldn't turn off the dining room chandelier lights for three days while I figured out the box they'd stashed in a cabinet had a radio transmitter that talked to the light. A while later I paid an electrician to run some wire through the ceiling and a wall, and install an outlet with a switch.

There was also an outlet in another room with some complex controls. It stopped working after a while. Turned out the switch - which is connected to a freaking electrical wire - required a battery to work. I had that taken out too, and good riddance to all of it.

Meh, the furnace is perfectly operational and you could hold a screwdriver across two terminals to force it on. Not convenient, but not dire need.

The first-world problem is not the "staying warm" issue, but the fact that the fancy 'IOT' thermostat requires an internet connection to set.

In "third-world" areas, and even in many modern "first-world" areas, a heater can be manually turned on with a simple switch, regardless of thermostat settings, and just as easily turned off. The lack of these controls on a significantly more expensive thermostat is where the first-world problem creeps in.