This is a problem because each of these stores use their own proprietary client. If instead they all used a public API then there could be an open source client that can access any of the stores.
We of course already have a possible client: the web browser. It works great for all sorts of e-commerce sites. It just doesn’t work for installing games from these stores. That could be changed, though.
I think if Apple is forced to open iOS to alternative stores, then I would like to see an API based approach. Force all the stores to compete within the same app, so they’re only competing on price and selection.