I am not a mathematics educator. But I did take junior high geometry that covered all those topics. Here's a student's perspective.
I don't see a topic on that list I regret studying. I always thought studying triangles in-depth made it easier to appreciate the role of triangles in defining the trig functions. I took Trigonometry freshman year of high school. If I had just learned SOHCAHTOA alone, I would have never appreciated the important the properties of right triangles versus nonright triangles. For me, my first look at trig was seeing how geometry could give me a new powerful mathematical tool (ie sin cos tan) through the geometry I has learned. Thus, understanding many properties of triangles gave me a better appreciation for how trig functions are defined and why right triangles are useful for that. I thought trigonometry was beautiful in part because I was so familiar with triangles.
That said, I feel my future math courses never used much of the geometry I learned in that course. I have never used SAS or SSS ever since then. In fact, triangles were one of the few things I actually used after that course. Only many years later when I began studying differential geometry and non-Euclidean geometry did I really feel a curiosity to revisit the principles I learned in my geometry class. And I personally always was disappointed by this. Now that I reflect on it, most courses I took in high school I have used. Geometry would be an exception in that much of it I haven't used.
So perhaps if curriculums made more use of non-triangle concepts, it would be worthwhile to study stuff besides triangles. But, especially if you do physics or anything involving Fourier methods, you want to have a good grasp of trig and I feel triangles are a key piece of that. In other words, I wouldn't change how triangles are taught unless I see topics I know will be more useful that should replace them.
I actually would have liked to study stuff besides triangles more in-depth. So I am not necessarily pro-triangle. But I am always trying to invest my time in things that are useful and triangles clearly were the most valuable part of my geometry course.