In some cases, you’re absolutely right. And in others the CEO is responsible for those things. That works, to a point, and it’s changing. Having been in all three roles, as CTO I’d rather be building the technology and the tech team. As the CEO I’d rather be building the company.
To answer your question — A CTO would prefer working with a CPO so that they can focus on the aforementioned tech and team. Again, the way we build products is changing, and we’re relying more on customer and market to determine what we build. Those things can certainly be the purview of the CTO if that’s how the company wants to roll.
Finally, this shouldn’t be a responsibility of the mid-tier tech manager, as they lack authority to make changes or stop changes to the product.