I was a very hands-on CTO for years after a decade of coding, and broadly enjoyed it. But as the teams I managed grew it became increasingly unfulfilling. When you're CTO, you're often excluded from business decisions which have a bigger impact on your team than any tech innovation, and the input you do have can be hard to relate to the shared business context of the CEO/COO/CFO.
So I went and got an MBA (Harvard).
Now I know exactly how to frame (and improve!) my non-technical contributions, have much more context on what "success" means, and have the credibility to really be a part of the senior team.
Unfortunately, there's no real place in the world for a highly technical business leader. You have to leave code behind at a certain point and spend your time on people/financial/planning issues. The ultimate end of that road is CEO, and not everyone wants to go there.
Also, I'd really misdiagnosed my malaise. What I'd been missing was not strategic input, but the opportunity to build things. To weave together inspiration and ideas into innovation and growth. I love building things and challenging assumptions, it fulfills me.
Now I'm off to start a new venture as a solo entrepreneur. The only truly successful technical leader is the founder, and that feels right. My last day at my day job is June 30th. :)