Why does chacha20 not use bitwise not?

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:

1. Why did Bernstein went with constants rather than bitwise not?
2. Would use bitwise not once every two rounds, for example, cause some kind of issue that I am not aware of?
• using a bitwise not is the same as adding a constant of 1 – Richie Frame Jan 29 at 19:48
• @RichieFrame I am aware of that. – 8321992485 Jan 29 at 20:10
• which cipher uses bit wise not for eliminating fixed points ? have you seen a particular cipher? – hardyrama Jan 30 at 3:22
• @hardyrama Xoodoo-p and Keccak-p, although these are not ARX, unlike Chacha20. – 8321992485 Jan 30 at 16:20
• @8321992485 keccak uses a LFSR to generate constants, and im pretty sure it does not use NOT – Richie Frame Jan 30 at 21:32