The purpose of a hiring process (as in take home assignment) is to see that the person is competent to do the job. It was already established that he was. So following a formal process is a stupid waste of time (on both ends) that has nothing to do with strengthening the company and is simply an unnecessary ego trip. The company disqualified itself.

It's one possibility, and I would bet money that it happens sometimes. I itemized it last because it seems the least-likely of those possibilities.

I think it's kinda intuitive that this could happen. Startups tend to require early people to figure out and apply a ton of diverse skills. You can guess many founders will think "I'm hiring my friend, and I don't know how the power dynamic will work out". And some percentage of those will then think, "...so I should establish from the start that they're the employee, to avoid problems later." And from there you get the dance-for-our-approval tests that so many techbros have cargo-culted.

Tbf the hiring already said they don't have the position open, and rather than doing something about it, the CEO asked OP to make another homework, which is also not a guarantee. Another round of interview may be fine, but another homework, that's laughable.

OTOH, it may be that the company already have one or some super programmer, that he/she carry the company to success. Having OP, if we assume is another super programmer, may halt the company rather than improve it.