Only other alternative I can think of would be an Apple App Store-style review process where the task of proving trustworthiness gets shifted onto the developer rather than the user. But it's still based around human trust rather than a platform constraint.
On the matter of websites, if the decision rests on individual choice, then individuals certainly have a choice to visit (and thus trust) a particular domain name and cert. That users need merely type in a name, and that there's a giant company helping you search for these apps, simply means that web apps are easy to find and install (and native apps are only slightly harder to install).
Then there's the role of the app stores, which I imagine practically deals with the supermajority of garbage, spams and scams out there. We could also have orgs whose sole job is to maintain lists of credibility, if that's what people want. Then a web user could download a browser extension or use a browser that subscribed to these lists by default. In some ways that's what ad blockers are, except ad blockers are even more precise and there's nothing quite like it in the native world.
Installable programs grant a degree of trust over your system.
If webpages are unsafe, or have native capabilities, the World Wide Web becomes less useful, as the act of clicking a link is heavy thing.
Related note: this is also why iPad and Android tablet apps don't have real popovers or floating toolbars either. Mobile treats the window boundary as sacred.