I'd argue entirely opposite, that a dead man's switch should 100% rely only on someone else's services and should avoid any dependencies on your stuff, as something happening to you is correlated to something happening to things you run or own, and the whole point of such a switch is that it should function properly when e.g. all your stuff burns down or gets confiscated or whatever.

Okay, so now your dead man’s switch depends on your home or colo’s power, internet connection, compute hardware, storage hardware, network hardware, software stack maintenance, plus the ability to pay bills for those on time?

Pre-Paying a cloud service pennies per month to do all that for you will likely be more reliable and much simpler.