Unless Apple or Google want them to.
Over the last year I’ve seen a half-dozen or so “HTML 5 App Stores” looking for funding — I always pass. Why? No one cares. Apple and Google have trained us to use app stores. When my mom gets her shiny new iPhone 5, she’s not going to remember the name of some misspelled obscure HTML 5 app store, browse there, search, launch the app, then add it to her home screen. Sorry HTML 5 fans, the hurdles are too high for most consumers. The only way the masses will ever care about your HTML 5 app is if they are redirected when browsing your site (eg. m.yoursite.com) or Apple/Goog decide to allow them in the App/Play store.