... could be modified, very simply, to read updates for additional software ...
It's only so simple when you have a single binary file with no dependencies running only on the developer's machine.
Beyond that, it's quite a complex problem. I could give you a list of about a thousand major problems that need to be solved to make a "one size fits all" updater. Plus, it's not in the self interest of either Microsoft or Apple to allow update installation from unverified sources.
... similar store for Windows in their own update service ...
The store has been tried before (once by MS, many many times by 3rd parties). Each time it was a failure. Largely due to the uncoupled nature of the "Windows ecosystem".