I don't even understand what that means. What programming problem?

If you rarely need an API but set something up like this just to rarely use it, it seems one needs to write their own code for this functionality and not go through hoops to run someone else's. That just sounds so bizarre.

Not someone else's API, your own. You make an app. It needs an API that you create (perhaps to sync up scores or something). You don't want to run a machine full time just to accept one score update a day.

Same issue. If one needs to spin this up just for a one-off usage, there's something wrong that needs to be fixed.

I’m not sure how to explain this so you’ll understand. It’s basically how all phone apps are written. It’s a common pattern.

If you made a iPhone game and wanted the high scores to sync to a global scoreboard when the game is over, how would you build that?

What if you only expected 10 players a day?