I guess ply was the best material way back, and MDF is a pretty recent (comparatively) material. The stuff has been banned in the US I believe for quite some time due to poisons used in the manufacture. Given the way it fails to do its job all that well  in the building side (put a drop of water on it and watch it expand and turn into crap) I can't imagine wanting to use it in a pinball (not that water is used, but you wonder what some Novus 1 might do). I think ply due to its construction has a tendency away from warping.

My brother is a wood machinist by trade, and has said to me many times that MDF is illegal in Europe due to the poisons in the glue. The European version of MDF must use a water based glue.

I'm not 100% sure why ply wood is used either, but I do remember something about using "Marine Ply" to make pinball playfields... not really sure why Marine Ply would be needed though.