Well, outside of when GH goes down, managing this in the cloud allows you to make more stuff 'serverless' - you don't have to worry about hardware failure and the maintenance burden that comes with moving stuff [data, code, secrets, logical volumes, etc] to a new host when you need to decommission the existing hardware. As long as you commit to the repo manually every few months (GH will stop crons on repos that have no commit activity), GH will continue to run your code on good hardware.

The idea behind the "serverless" approach is a lightweight process which doesn't spend any measurable CPU / memory (at least for healthchecks). GitHub Actions is the opposite of that. After all, cloud is someone else's computer - in this case, several other projects can use this computer for something more important than health checks.

While I agree using Github is a bad idea for a status page, using any machine on a home network is an absolutely terrible idea.

What's the point of monitoring unless you can get paged about outages?

not to mention when, not if, github goes down