I think the question is, given that someone can do one of those things really well, how likely is it that the same person can do the other really well too?
It seems obvious that the kind of traditional business ceo that investors often want to find to replace a founder is not going to be successful as a starter. Let's just accept the common assumption on that one.
I'd argue that what makes a great startup founder often makes a terrible leader for large corporations. I think every great founder has a reality distortion field (https://en.wikipedia.org/wiki/Reality_distortion_field) which projects their vision, keeps them pursuing seemingly bad ideas in the face of insurmountable odds and allows them to overcome the biases and assumptions that dominate so many business decisions.
Some leaders expand and adapt this to build great, crazy companies: Steve Jobs, Elon Musk, Zuckerberg (maybe). Often they also create a cult-like, maybe toxic, certainly messy corporate culture that still somehow succeeds.
Others can't do this: Travis Kalanick, Elizabeth Holmes, Parker Conrad. They let their "startup founder, growth at all costs, thumb your nose at the rules" attitude destroy their company culture and embroil them in ridiculous, easily avoidable legal issues.
In my experience, a corporation's culture is the manifestation of the most extreme personality traits of its leaders. There is a time, when crossing the chasm, that the exact traits that made the company grow rapidly and the founder extremely successful are the ones you want to suppress to create a stable, efficient and effective collaborative endeavor involving thousands of people: a corporation.
I think (and this is due to some reflection on my own ideas) that if you reject the idea that there comes a time when a company should abandon "burning vision" in favor of stability, process, predictability, and broad appeal, you're actually rejecting the idea of a corporation as a hierarchical system of power deployed to efficiently organize the work of thousands of people. And I'd probably agree with that. The traditional corporation needs a traditional ceo but it's a damn shame that every revolutionary startup has to end up as a traditional corporation.
In other words, you can't use a broken system to criticize leadership.
Second, if they do learn that skillset as the company grows, then they would be a great man/woman for that job.... at their next company. For this company, you'd want someone who has it right now, not someone who'll learn it halfway, from costly mistakes.
There's nothing classist about it. You could train an army corporal to become a general. But you can't just take an army corporal all the way to the experience needed to become a general in a year or two. It takes generals 20+ years before they have the skills to lead thousands of soldiers. To suggest that any reasonably smart corporal can go from leading a squad to leading a division in a few years of on-the-job training is just ludicrous. If I'm wrong, then please provide some data. Actual data, not anecdotes.
Nobody is saying that a corporal can't ever become a general. The suggestion of classism is implying that a corporal can't become a general because he's not of the right class. Of course a corporal can become a general (at least in the US Army) -- which is the very opposite of classism. We're just saying that a corporal doesn't become a general through a few years of on the job training and that a corporal doesn't become a general while on the battlefield.
What I'm saying is that a good large-company CEO is gets those skills over years of experience. If a founder-CEO slowly scales, then perhaps on-the-job training would work. But when an org goes from 10 people to 1000 people in a few years -- it would take an extraordinarily lucky person to be able to handle that transition without prior experience.
There is nothing inherently special about someone who runs a small vs. big company, except for experience. I agree with the poster above: classism at its finest.