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.