Hmmm... the market is kinda narrow.
But more importantly, say I self-hosted this service, then, I have to answering emails for the rest of my life telling a program I'm still alive. It's kinda high maintenance all on it's own.
That is assuming this service continuous to run without upkeep, at very least keeping it powered, and connected to the Internet. I'm not really sure what comes first, the end of my life or I got bored of doing it.
I know it sounded inapplicable for a lot of people especially who do remote works, but still if you're thinking about letting a machine run your death plan, maybe it's also the time to start make people connections, such as with lawyers, partners etc, people you can trust and have the capability of handling issues.
Also, if you do remote work, maybe setup an account inheritance plan if the platform supports it, assuming the account is dedicated for working for the effected team of course.
Also also, just an idea, what if you make the check passive? Instead of having to answer emails, some automated procedure will send keepalives to tell the program to not trigger? That will massively lower the cost of using it.