[ruste]

I don't think this is as much of a constraint as you'd expect. Imagine you manage to pull 1 psi over a 10x10" patch of box. That's 100lb of lifting force. If you're worried about whether the cardboard can handle it spread the area and lower the pressure more. I don't think 1lb per square inch of cardboard would be an issue and it looks like they have more surface area for suction than that.

[BugsJustFindMe]

Without bottom support, contents might fall through an inappropriately supportive box.

The answer is "no, not all boxes, but yes some boxes".

[dijonman2]

Last time I moved I spent a fortune on double corrugated boxes. I bought a cardboard stapler and taped it.

Heavy boxes still needed support from the bottom.