If you need it for CI/CD of some kind, then APIs, networking, access control, and security (including, possibly, physical security) are all important too, and not trivial to do with a machine in your closet.
Paying by the second is also ideal for these use cases. You run a build occasionally, but it mostly sits idle.
Just run ZeroTier on the Mini and join it to your network. That's what we do. Of course we are ZeroTier so this is how we roll. Anything with an Internet connection is in "the cloud." We just donate all its spare cycles to Boinc. :)
Pay by the second would perhaps be preferable but unless I am reading this wrong you have to pay by the hour and it's relatively expensive.
It's too early in the morning for me to try to parse an AWS pricing page, but according to another comment: "You have to pay for 24 hours up front, after which they bill by the second."
Paying by the second is also ideal for these use cases. You run a build occasionally, but it mostly sits idle.