What about the benefit that the web brings to updating the user's install? I know that it is technically possible to push a new Java or .NET app out to users.
I've done it. The one thing it requires is a lot of coordination. Notify the users to keep their equipment on the network from time X to Y. Notify the infrastructure team to schedule a push. Have the dev team on standby in case the push goes bad. Have the software protect itself when inevitably someone's install is corrupted or skipped.
Compare that to the web. User opens Chrome; they get the new app. No push. No real notification of any team. Hell, Ops probably doesn't have to be notified if they automated web app deployment to servers. The whole thing is very easy. Even if you have the added complexity of a Chrome-app wrapper, still pretty easy.
Given the ease of deployment and the mitigated risk of data corruption due to version issues of the app, the web looks pretty good. Given the advancement of hardware and software, UX can be close to native. If not native, app-y for lack of a better word.
If it lacks UX for native, don't target native. Target app-y. This is between native and document. It might become complex to manage local state, but that shouldn't be a deterrent.
Tangentially related, to the general question: does the user want to have a link to your product on their desktop? The answer is probably no. They want easy access to your product, but the link conflates how this occurs with a sense of permanence. Your app is not the product. Your app is tool to get the product: information. UX and installation are both just means to the end.