1) Convergence works great for "casual" apps - messaging, stores, content feeds, etc.; anything where the amount of stuff you need to see on screen at once doesn't need to be especially large. But the web already does a great job of making this type of application both responsive and cross-platform.
2) Advanced, dense professional tools will never adapt automatically to mobile screens in any meaningful way. And frankly, these are all I find myself installing natively on my desktop anymore.
The vast majority of software these days falls squarely into one of these two camps, and neither seems to benefit much from the prospect of convergence.
However, I think you should think of this in a different light: Purism's real problem is: How do we bootstrap this device?
That is to say, there is simply not enough money / engineering talent to both develop all the hardware AND all the software needed to bootstrap this thing. It must appear "viable" to the public as a 1.0 product.
Therefore, using convergence to bootstrap the product and then building out native UI's in further versions is probably the best decision.