The anthropic principle has nothing to do with why complex numbers are necessary for doing quantum mechanics. Complex numbers are purely abstract objects and yet are necessary for giving a proper account to the real world.
"From all of this I am forced to conclude both that mathematics is unreasonably effective and that all of the explanations I have given when added together simply are not enough to explain what I set out to account for." - Hamming
Most of mathematics has no use whatsoever in physics. Physicists select the mathematical tools that best enable them to build their models. In other cases, the necessary tools do not exist and they are built for purpose.
In many cases, physicists are not so successful. Look at the current debates in particle physics and the grand unified theory. Progress has largely stalled.
In other cases, models are revised continually as new information comes to light. For example, the age of the universe as we know it may double [1] from 13.79 billion years to 26.7 billion years.
You might call this “unreasonable effectiveness,” I call it a process of messy refinement and rethinking over thousands of years, much of it later shown to be invalid, despite mathematical correctness.
Again, and last time: the fact that you can use mathematics to do physics to the point we've been able to do implies something about the universe. You should think about it a bit more.
"From all of this I am forced to conclude both that mathematics is unreasonably effective and that all of the explanations I have given when added together simply are not enough to explain what I set out to account for." - Hamming