Honestly, it's not far off from a typical CTO role. Being CTO is about connecting the technology side of the company with the vision and business goals of the company, and making sure the two match. There are great ways to structure the technology and build out the product that don't contribute to the business goals or even the vision of the startup (and can even be opposed to it), and there are sometimes less-than-ideal ways of building the technology of a company that get it where it needs to be when it needs to be there.

The CTO's job is about half technology and half business when it's a small startup. As the startup grows, you can't possibly make every technology decision, and so your job is more about getting the right people in place who can make the best technology decisions on your behalf as long as you keep them appraised of what the business needs are driving each of their decisions. And because getting those people in place and managing those people is almost all on the business side, your role becomes more about active business management while maintaining an in-depth awareness of the technology so that you can step in and correct course as necessary.

These are all just generalizations of course, as every startup is different. I imagine if you're the CTO of a startup that caters to software developers and code, you probably get to continue devoting some portion of your time to coding. Even in other startups, I've seen a lot of CTO's (myself included) get to actually do some code occasionally, but it's more like once every 1 to 3 months, which sounds about in line with what you're doing.

I think the CTO role you desire does exist, but it's in a specific, somewhat narrow stage for a startup. It sounds like you desire to be a co-founding CTO of a very early-stage (possibly idea-stage) startup. I think your desired traits for the responsibilities of a CTO can also continue to exist years into a startup's operations if the startup remains bootstrapped and self-funded.

From my experience (both with bootstrapped and venture funded startups), when a startup takes venture funding and forms a board, the CTO role becomes more about managing expectations, facilitating understanding of the technology to the depth needed to those who need to understand it to make the proper business decisions, and more importantly, contributing to and making the business decisions that require the knowledge of the technology that only you bring to the leadership and management team. The smae change in responsibilities happens to bootstrapped startups that become big enough, but the change is more organic and occurs over a longer period of time (which actually makes sense when you consider that venture funding is intended to make non-organic growth occur over a faster timeframe).

More cynically, I guess this management of expectations and facilitation of communication could be described as "dealing with everyone's crap," but really, it's probably what the startup needs. If you truly think it's not what the startup needs, then speak up! You are the CTO after all, and that's now part of your job to make sure the company is making progress. But recognize that the business side of a startup is as important (often more important depending on what the startup does, how it's funded, what it's milestones are, etc.) as the technology side, so make sure you understand the importance and motivations of what everyone else is trying to accomplish in the company before dismissing their actions wholesale.