I have a couple of 20" Dahon bikes, one with full suspension and one without any suspension.
I would absolutely agree that for most roads and smoother (hard packed) trails the suspension is not at all required.
My suspension bike does have slightly wider and lower pressure tyres than on the other bike, 42mm at about 75psi vs 35mm at about 80psi, but I doubt this makes a huge difference, so the suspension does seem to be fairly noticeable.
The suspension isn't soft, little bumps or a rough surface is felt, but in comparison, where the road surface isn't good, the ride without the suspension definitely feels harsh. Small holes, ridges, speed bumps, drains, etc can be quite jarring, especially at a brisk (not fast) pace, even with all one's weight lifted off the saddle.
I find the suspension gives some options for rolling over/down smallish bumps that I'd avoid with a shorter, smaller wheeled bike that wasn't very "solid", and definitely gives a bit more confidence when encountering some unexpected roughness or hole or something.