I think Native Apps are the only way to go.
Since Unity charges for the Android and iOS export, I doubt they have any desire to develop a WebPlayer plugin for the platforms.
Even if they did, the web player builds don't handle touch input, so that would require a unique WebPlayer build for mobile browsers. That's not to mention the code generated for web builds is optimized for desktop video cards, not mobile ARM chips.
Even they did go through all the work needed to make this work, iOS web browser does not allow plugins, so they would be restricted to Android devices and that platform already allows for users to install web downloaded apps anyways so there is no real benefit.