Right now chacha20 and blake use constants in order to eliminate fixpoints. As far as I know however inserting a bitwise not every $n$ rounds should eliminate this issue without using constants (and as a bonus chacha20 would be a $\{0, 1\}^{512} \to \{0, 1\}^{512}$ function rather than a $\{0, 1\}^{384} \to \{0, 1\}^{512}$ as it currently is).
My questions are:
- Why did Bernstein went with constants rather than bitwise not?
- Would use bitwise not once every two rounds, for example, cause some kind of issue that I am not aware of?