Many apps should not need an active internet connection. You can't do local first / offline first. Users don't own their data, need to give up on privacy, and you require more trust of them. Users are always forced to upgrade, and don't control the upgrade process...
You also incur recurrent server cost that need to be passed down to your users (as a matter of fact, I suspect that some web apps are an excuse for a subscription where a one-time payment would suffice)
You'd have other problems too, like browser compatibility, etc. I don't think "we run remote webapps all day without effort".