I think its good for users to associate "App Store" with a generic place to find and download applications on any platform; like the terms "program" and "browser" it helps to have standard ways of communicating basic concepts of computer/device use. Its a benefit to _everyone_ (Apple, Android, Microsoft...) that users can more easily interact with their systems sans training.
Trademarks and branding are strange things. One would assume that giving a term wide-spread use would be beneficial to everyone, but it seems that it's bad for companies. I still don't quite get it myself...
Because you can lose legal muscle behind your name if it becomes such common use that users might use the word without knowingly referencing your company's brand.
It would be an interesting case if Google ends up becoming a legally generic term for search engine. Would the company end up changing it's name? Would there be Microsoft Google (formerly Bing) and Google Google?
