That's still assuming that they're competing as consumer tools, rather than competing to discover the next miracle drug or trading algorithm or whatever. The idea is that there'd more profitable uses for a super-intelligent computer, even if there were more than one.
But would miracle drugs and trading algorithms be as profitable as AI research/chip design/energy research? Probably if AI is by far the biggest growth in the economy majority of the AI's usage internally should (as incentivized by economics) in some way work towards making itself better.