The Common Core State Standards for Mathematics (CCSSM) provides a list of standards that should be covered; the inference that a topic not mentioned in the algebra strand should, therefore, be omitted does not necessarily follow, although time constraints no doubt ensure that will be the case for many courses.
Rather than going into the process for developing CCSSM, I believe it may be helpful to wonder about the '2' in the course title: What exactly is meant by Algebra 2?
It follows a course called Algebra 1
It precedes a course called Algebra 3? (No, unless you mean Linear Algebra; followed by Abstract Algebra; then Abstract Algebra 2 = Galois Theory; then Algebraic Geometry or Algebraic Topology or Algebraic Number Theory or...)
It precedes pre-Calculus, but doesn't that make it - for all those who eventually take Calculus - fall under the umbrella of (literally) pre-Calc?
It is pre-Calculus, and the next course is to be Calculus
The last two points are especially important: Is this course leading in to a follow-up course that examines further function families (e.g., rational functions), trigonometry, and other topics? Or is it headed straight for secant lines that segue into tangent lines and eventually limits in a first course on Calculus? Alternatively still, is Algebra 2 supposed to position students to make a decision around whether they should continue on a path to Calculus or Statistics/Probability? This could have an effect on topics for inclusion.
In fact, could Algebra 2 be expected as a terminal course? For some US colleges/universities, yes, this is the expectation; in fact, some do not require even Algebra 2. Consider this piece from Inside Higher Ed:
Michigan State University has revised its general-education math requirement so that algebra is no longer required of all students. The revision reflects an increasing view on college campuses that there is no one-size-fits-all math curriculum -- and that math is often best studied in connection with everyday life.
(I note with no irony or sarcasm -- only interest -- that MSU truly has one of the best programs in the country/world for mathematics education.)
Returning to your list of topics, it would probably take me a full year to cover a proper subset of those topics in ways that are mathematically meaningful. If you will permit a mixed-metaphor, then I note that one can "cookbook-blitz" these topics by asserting facts and having students carry out various procedures (e.g., transforming trig identities into statements about just sine and cosine, and then using a very select few axioms to prove the desired consequence). Personally, if I were to teach about trig identities in a way that felt meaningful (in some ways) to me, then I might opt to use them as a way to introduce more formal proof writing (cf. my answer to MSE 2905643) but this would diverge from certain expectations around "mathematical maturity" in an Algebra 2 course, and it would take far too long for me to get to all the "omitted" topics in your post - as well as those that remain!
For a fun mathematical closer, here is one example of a cookbook-blitz approach to trigonometry: Accept the fact (whatever it means) that $e^{ix} = \cos(x) + i\sin(x)$. Consider next two ways to change the LHS to $e^{i2x}$:
Squaring both sides
Replacing $x$ with $2x$
Since each of these results in the same LHS, the corresponding RHS's must be equal. By accepting that fact, we arrive, then, at the following identity:
$$[\cos^2(x) - \sin^2(x)] + i[2\sin(x)\cos(x)] = \cos(2x) + i[\sin(2x)]$$
Observe that matching real and imaginary parts immediately yields the double-angle formulae for cosine and sine. Now, I happen to believe this is an interesting derivation (and you can use this to derive many other identities provided, e.g., you know a special value or two of sine and cosine from the unit circle) but I do not think that a one day lesson on this fact is an ideal way to build meaningful mathematics with (most) students. In particular, I am concerned that the given is too strong, and that the techniques (observing two ways of getting to the same LHS; matching real parts and matching imaginary parts) are too novel to be sprung all at once. Imagine instead a course that developed these ideas in multiple ways, and in which student discovery was centered rather than speed or initial efficacy. Under such conditions, I would not, personally, be able to do justice to these ideas along with all the many other ones that could fall under as broad a name as Algebra 2.