Look at this analysis of the Falcon 9 flight profile, in particular the graph at the bottom right: https://www.reddit.com/r/spacex/comments/6303ko/falcon_9_ful...

The majority of the horizontal delta-V is produced in the second stage. The job of the first stage is to a large extent just to lift the second stage out of the densest part of the atmosphere, to minimize drag for the second stage. A plane can do the same thing, and possibly more cheaply in certain scenarios (well, that has to be Allen's plan anyway).