I'm on OS X right now, and I use Spotlight for absolutely everything. The help menu has a feature to Spotlight within menus, but it's not great if you don't know the literal name of the command (like save or open). Things can get complex quickly in robust applications.
What about appending alternative names to menu commands as metadata, so when a user searches for 'paint bucket' in Photoshop, they're driven to 'fill'. I'd imagine that's the easiest way to map intent to action. Further still, make menus public data-driven — learn common intent by what users search for and end up clicking on.
The use cases for this might be small, but the benefit of keyboard shortcuts is in discovery. Users should be able to articulate to applications what they intend to do.
Edit: If this exists already, we're living in the future.