> 2) resist the urge to impart correlations into the generation

I think the opposite. The more dimensions you have, the more "invalid space" there should be. Otherwise you end up with giant dinosaurs with tiny feet and fairy wings. You end up with a yellow kitchen with a barrel full of arrows next to a blue dungeon with a giant dresser. You end up with nothing making sense, and everything feeling random in the same way. Trying to spot the differences between 100100111101011110110001001011101 and 1101101110111010000100111001011101 is exactly the "bowl of oatmeal" problem. The vast majority of possible combinations of values should be invalid and impossible, otherwise the choices actually don't matter.

Agreed. Elsewhere in this conversation people mention simple games that procgen well: Spelunky, Terraria, Dwarf Fortress, Dungeon Crawl Stone Soup

These are games painting with a 16 color palette while the technology exists for any shade in RGB. The more variations, the less likely things will be coherent (let alone brilliant)

I mean, almost no games have that many meaningful dimensions in the first place. It's more likely that the correlations you add just reduce the potential for interesting combinations to arise in the first place.