- Sandboxed, web apps can't wander around in your filesystem, and you can even prevent them from knowing anything about you (private mode). That's good for privacy and security.
- You bypass the apple/google store, their paytoll, capricious criteria and how they promote apps
And I think asm apps (not websites) will have a great success when asm has become a full VM not just because of these reasons, but also because it will make it possible to develop cross-platform in a language that isn't javascript. Some people love javascript, I personally hate it. C++ devs will be able to develop in C++, I expect C# and Java dev to be able to write their apps in C# or Java, and I am sure even more languages will join the party. That's a great thing.