Remember the post about needing to support Firefox?
The same thing goes for browser-based functionality in web services. If your service offers significant functionality that is only available in a mobile app, but doesn't depends on any particular mobile-specific hardware that wouldn't be available on desktop, it is broken. (And, as we discussed before, it's okay for a project to be a little bit broken when it's in its infancy — but a mature service with the resources to support a wide spectrum of platforms should know better.)
Maybe this is just the mad ravings of someone who types faster on a real keyboard than on a phone, but still wants to send messages on <insert service here> without relying on a third party plugin, but it seems reasonable to expect that web-based services should be accessible from the browser. Not everyone is comfortable using a smartphone for the majority of their daily communication. Not everyone even _has_ a smartphone (or a big two smartphone that can run a native app, at least).
At any rate, if you're designing the UX for a new software product, keep in mind that some of your potential users are still desktop-first, and are unlikely to switch at any point soon. Smartphones are good for some things, but there are still a lot of tasks for which a full-fledged computer with a real keyboard can't be beaten.