This already exists, and it's called Bodega. It hasn't caught on. There's also MacPorts and Homebrew, which are popular among devs but have no presence among regular users because they're for *nix command-line tools.
I believe the reason open app distribution systems like APT work so well on Linux is the "open culture": the vast majority of software Linux users want to run is Free Software. But can an APT-like system work as well with proprietary, for-sale apps? I know there are proprietary drivers and such on various repos, but I'm talking about stuff like Photoshop, Office, or the thousands of little paid apps you can get on iOS.
Yes, it'd be great if Mac users embraced FOSS more, but they won't do it as long as FOSS lags in ease of use and polish. And it will continue to do so because polish is hard work, and devs working for their bread are more willing to dish out the elbow grease. I'd love for this to change, but I don't really see how it can.