You are comparing putting a wider chain on a narrower chainring, but the opposite does not work. SRAM road (flat top) 12 speed chains (and from what I've read) Shimano road 12 speed chains are narrower at the rollers and inner links than previous 5-11 speed chains, so when you put one of those narrower chains on the 5-11 width chainrings they don't fit very well. Like trying to push a penny into a dime width slot.

https://www.evo.com/chains/sram-riva...12-speed-chain

Up until 12 speed road, all the different chains worked on all the different chainrings because they were only different widths on the outside.

So the crankset does care.