I personally have problems with doors, and stuff that should be locked. I can never be sure I locked properly. Totally did backtrack unreasonable distances just to check if I had closed the door. It's all fine when it's my door. Worst case scenario, I get robbed. However it's more of a problem when it's someone else's door. Worst case scenario, they get robbed, and that's a different story. Or pets get out... Obvious…
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.
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.