Do independent web apps have a future in world divided into walled gardens?

Today, most computation is still done with general-purpose computers. These machines, primarily laptops and desktops, are "open" in that you can install and run on them whatever you like, and you can build for them whatever applications you like and distribute them in whatever manner you like. The inherent openness of these platforms has also served to make them incompatible with each other and even with themselves; just getting an application to run on different versions of the same platform (eg windows) can be a pain. For this (and for other) reasons, over the last few years much application development has shifted to the web.

But now it seems the tide has begun to recede. Application development is heading back towards native apps, particularly native apps for a single, closed platform. It appears we may be entering a future where the whole technological landscape will be partitioned into any number of walled-gardens.

My question is basically this: if the future is the iOS and other closed platforms like it, does it still make sense to build a business based on web apps with the expectation that such a business will still make sense two, three or five years from now, or is one better off taking the plunge and basing your business on a platform like the AppStore instead?