What happened to just good old OS APIs? You could wrap the entire "secure update" process into a function call. Does Windows somehow not already have this?
The problem is finding and installing new software. Without a well-known official repository, people end up downloading Windows apps from random websites filled with ads and five different "Download" buttons, bundled with everything from McAfee to Adobe Reader.
We should be asking how to enable adding external sources like Ubuntu PPAs (which can then be updated like the rest), not whether there should be an official repository to bootstrap the package manager in the first place. "Store" is just a typical name for such a repository, it's not mandatory.
The Store uses that behind the scenes. You don't have to use the store to use the system update system.
It's particularly good because updates can happen in the background, without having to launch your app to trigger them.
The problem is that this needs strong regulation to prevent it from turning into a payola marketing scam where vendors have to pay for placement.