Interesting... My initial reaction about the startup looking for a CTO was the same as yours. I was a founder and CTO, so it seems odd that you would not already have that in the mix... however I can see how there could be an idea, a market, a sales strategy, and a tech idea without the actual tech. In that case you would need to find a CTO to build that tech.
Of course the real gotcha is that there is no 'idea, market, sales strategy' that will be perfect, and the work is finding out where those ideas are wrong and fixing them. The lessons from my successes and failures says it is only worth doing that as a founder, because the failure risks are both high and unpredictable. Time is expensive, so spend it where there is both risk and reward, not just risk.
The most successful startups that haven't been founded by technical people I have seen usually didn't even have much of an idea - but they had customers and kept talking to them and created a product vision out of that. All startups should be doing that.
Of course the real gotcha is that there is no 'idea, market, sales strategy' that will be perfect, and the work is finding out where those ideas are wrong and fixing them. The lessons from my successes and failures says it is only worth doing that as a founder, because the failure risks are both high and unpredictable. Time is expensive, so spend it where there is both risk and reward, not just risk.