I think lazy susans waste a lot of usable space in a cabinet. I like to get everything possible into a laundry room cabinet and would never ever consider lazy susans for that room.

Can you reach into those corners easily or will they become caves for lost items? I have a kitchen with many unreachable corner cabinets and I would love to have lazy susans there. At least some of the space would be functional. New cabinets would be better, but $$$ is an issue.

I am very envious of your nice laundry room - my W/D is stacked in a closet in the kitchen. Convenient but not very efficient.

I can think of very little, laundry wise, that would fit in a lazy Susan. I would go with corner cabinets. Can the washer be moved to the corner? That would give space for a good size cabinet. 12" won't store much.

Like oreg mentioned, lazy susans are awesome for tricky-to-reach areas, like a deep cabinet. The original design of the LR at my weekend house was so terrible I couldn't actually get to the back of the shelves above the machines, so I used three. When I re-imagined the room I changed all that, so the LSs were junked! I make better use of the space grouping products by purpose in open containers.

Full disclosure: I'm a crazy who uses different detergents/pre-treat products depending on the fabric, color, etc. so there's a lot to organize vs. a typical scenario. Lol.