I agree: 4'x4'x4' cooks much better than 3'x3'x3'.
And it helps to be able to move the mostly-finished compost ahead to the next bin while the chunky undigested stuff stays behind to digest further.
I don't have enough raw material to make even ONE 4x4x4 pile, let alone 2-3 piles or bins. So I got by with one smaller pile, usually elongated. It would only be deeper than 30" shortly after I added new stuff. It would be around as wide as it was tall, and around 3 feet long.
When I turned the heap, I would rake the outer dry layers to the left to continue cooking. I would add more raw materials, especially greens, on the left end to help the chunky stuff digest.
And I would rake or shovel the inner and deeper layers, mostly digested, to the right. When I took compost, I would take it from the right end and screen it. I'd return any big pieces to the far left to keep cooking.
Anyway, that's what I did until the park management sent in a crew to chop down anything my neighbor didn't like, and steal my compost heap!!
They chopped my bamboo like a HEDGE and stole my compost. GRRRR!!