I started reading and thought "why not just …"—and you did!
Since this is Hacker News, I'm surprised that you haven't come up with some more elaborate system, e.g., properly locking the door closes a circuit, and you can check the status of the circuit remotely.
I don't worry too much about whether I left the door locked or unlocked, but suck a system would produce anxiety in me, because I could never be sure if there wasn't some circuit malfunction and it wasn't showing me a false positive or negative.
My wife and I had the exact same response to the baby wearables or gadgets that promised to tell us if our baby was still breathing up in her crib. We weren't worried about that, so the notion of adding something that would almost-certainly be a flaky indicator seemed guaranteed to increase anxiety.
Since this is Hacker News, I'm surprised that you haven't come up with some more elaborate system, e.g., properly locking the door closes a circuit, and you can check the status of the circuit remotely.