It depends a lot on the specific business and company stage. E.g. CTOs at boutiques basically meet clients and put on a performance to instill trust. CTOs on product startups with little funding are more like "I'll hire a teammate that can put up with the mess I wrote". CTOs after the product startups have large investments are more like "I'll pretend I know what I'm doing and let the principal engineers actually run the tech and fix my legacy mess so we don't go out of business". CTOs at corpos are just C-suite politicians. Etc.
I find CTO as a title meaningless. At most it means they've got the signature powers.
I was CTO from 2 to 100, over 6 years, and led the core tech development the entire time. Tech Co-Founders certainly can and do code. I was a Principal Engineer before and after.
In a sense, you are right that the title is meaningless, and only means signature powers.
And you are right that other principals rewrote legacy stuff. But I also participated at the same level. I just knew I was only above due to some market luck lining up with my experience. Will never know exactly how much influence I had over that situation.
But I have a Jazz background. It is easy for me to respect equally everyone on the team. Sports can do the same, but I think music is probably more effective, because it is inherently more spectator than competitive. Musicians tend to make incredible team players, if they stuck with it for long enough. Many leaders in band are leaders in sports, in school. And the formal language abilities are already demonstrated in musicians.
I find CTO as a title meaningless. At most it means they've got the signature powers.