Warning: ramble ahead. I am not a statistician. This is based on my experience as a physicist-by-training exploring the more theoretical side of ML/AI.
Statistics is big. It's hard to answer without knowing what you plan on covering. I agree that most books (I've seen) suck. Wasserman all of statistics is the best I know, for my purposes. The problem I've found with most statistics books is trying to be too cute and clever by catering to a certain crowd thereby justifying holes that make it harder to truly understand and making the subject seem an incoherent patchwork.
The other problem that's even harder to solve is that the majority of people picking up a statistics book don't really think they need to learn statistics, just certain pieces. Which makes statistics seem less coherent and thus furthering the perception that statistics is in fact incoherent, leading to special background books that say "here's all you really need to know about statistics."
The final problem is statistics IS kind of incoherent as most often presented, especially when it tries to be what I'd roughly call "backward compatible". Why is so much time spent on p-values, for example? Is that really what a consistent modern perspective of statistics entails[1]? But backward compatibility forces it's inclusion, because that's what people still use and have used because they never got taught of "philosophy" of statistics, but rather rules. If you don't teach those rules everyone else uses, you're making them spend even more time on statistics than the small amount they're already unhappy spending. So the lowest common denominator is taught, which is incoherent. It's a vicious cycle that is not the fault of statisticians.
To an outsider there's not unifying dominant through lines because the field is justified largely through its application. There's no obvious "philosophy" or vibe of how to think about statistics. What I mean is that one approaching the field doesn't really grow more comfortable with it and doesn't really feel like they're advancing to a more coherent view, so they're less motivated to try to grok it, because it simply doesn't look like there is something to grok. With all of previous factors contributing to this.
So I guess the point of my ramble is that I think what's missing the promise of a reward for learning statistics "properly", really understanding it. In my biased view this is largely because it's not often presented to the non-professional statistics student as if there is a clear thing to understand, more just a collection of tools. And I think this is partly because the author already knows the reader doesn't want to spend time on it. So my advice would be, come up with a clear story of what statistics is. Promise and fulfill the promise that it is worth spending the time in a more abstract world for a little bit because the end is worth it. That it will save time and frustration in the long run because it won't just be a collection of basically faith-based tools with mystical rituals they will feel uncomfortable with for the rest of their careers. Tell that coherent story and then you can demand more commitment from your audience[2]. Maybe that cuts down your audience size but I think the net effect will be more people understanding statistics and what it actually is.
What would be the main threads and themes in your book? How would you justify spending time on it? What would require as necessary background? I don't understand the subject enough to offer any opinion. The most coherent things to me are convergence types and bounds. And then do you include computational approaches? For example in practice I'd say 90%+ of people would be better off using bootstrapping analysis for errors in most real-world cases compared to the standard "approved" approaches, but that's not very satisfying and the theory of it is certainly hard to integrate cleanly. TL;DR I don't envy anyone writing a statistics textbook.
[1] This is just a single aspect, but it gets to a broader problem. This is a really hard problem to overcome. So much of academia is taught p-values and to so much of academia that is basically the hardest math they know, and they work very hard to follow the rules they were taught, which to them is statistics. I don't know how you tell them to re-learn something especially when the answer is more math. That makes them even more hesitant and less likely to fully embrace a deeper understanding of the field.
[2] maybe that's the larger point. The analogy is maybe teaching calc vs. algebra based physics. Algebra based physics is harder to teach and learn, and it is less coherent and complete. There is not much meat in it, mostly rote tools. IMO conservation laws like energy and momentum and solving shit from there would leave a better taste for what physics is, but instead they are often used in one lecture to derive kinematic equations which are then elevated because students can memorize them. I guess it's better than nothing but it leaves people with the wrong impression of what physics is, just like I think most statistics leave a bad impression of what statistics is. Make the statistical equivalents of something like conservation laws the central objects. Something that makes it a coherent story that builds and rewards.