1. A html5 app is not necessarily the same as an online app.
2. A html5 app can detect the user agent (browser) and provide different UI's/functionality. Additionally, it provides offline storage.
3. That is indeed still missing in html5 (for security reasons). But the more something becomes desirable, the sooner it will be implemented.
4. Being reluctant to change won't get you any further.

That said, I understand your concerns but I think a paradigm shift is at hand. I, for one, welcome the ability to create an app that can be used on any device that is out there. And I admit that html5 is not yet at a point where it is usable for any purpose but it is heading in the right direction.
We are now in an environment where people want all their data on all their devices so I don't think it's wise to limit yourself to one platform. You must admit that it is a great thing to develop once and deploy anywhere.
This is an evolution you can't stop, in the end it's the user that decides how he wants to access and use his data. I believe that by stating (as a developer) that you won't follow this change, is holding yourself back. And we all now what happens to developers/companies that are reluctant to change...