Sure, most (if not all) software comes with a licence. Maybe I'm not using the best terminology. Maybe I mean "subscribing to", although that implies regular payment. Either way, what I'm referring to is the fact that Apple becomes a point in the critical path to just running your software. Whether intentional, or accidental, Apple can remotely prevent you from running the software you've paid for (e.g. [1]).

And I'm not even beginning to cover the terrible App Store app itself or the enormous cut Apple takes from independent developers.

[1] http://www.theguardian.com/technology/2015/nov/12/apple-user...

As far as I know, Apple can decide to shut down any app on their appstore if they wanted. Refer to the flux incident.

So I buy an app, and they can shut down the .app program on my Mac?

Theoretically yes.