I've seen koshi-nage adequately demonstrated and rationalized in several forms.
I accept the founders words that aikido is the form of no form based on my observations and experiences of nature and my practice in aikido.
I've also seen waves form and break in many shapes and sizes. They were all waves.
Bet you never saw a square wave, or one with an orange color with red dots. No, these don't exist.
You call it what you want, but you will be cut from behind if you do koshi nage like that...