If not a grand plan, then what? a few concentration camp commandants just all so happened to have the same idea of wiping out hundreds of thousands of Jews independently, sourcing the necessary Zyklon-B and so on, all in some off-the-cuff improvisation, like for the lols bro? and it just so happened that in every concentration camp and extermination camp, hundreds of thousands died. What a coincidence.
Nazi Germany was a repressive state of almost unparalleled brutality.
People who defied or went against the regime could (at the very least) be sent 'To The Russian Front'- punishment enough as a near-certain death sentence- and at worst they and their entire family could be killed. having first been tortured.
What would you say the odds are, of people improvising large-scale murder, in a hugely repressive state, without consulting their superiors?
Would you say Nazi Germany was a likely state for public functionaries to 'just wing it bro, lol'?