All these comments are very interesting and thought-provoking. Depending on the sources, it seems that, for the homebrewer, the ideal grain bed depth is between 4-12 inches. Perhaps counterintuitively, a deeper grain bed is more "efficient" (up to a point), but not necessarily "faster." See JP's HTB Appendices E and F for more details, if interested.
A grain bed depth beyond 12 inches might have compaction issues in a 10 gallon round Igloo cooler (internal dimensions 12 inches diameter x 18 inches deep) given that the height would then exceed the width of the grain bed. That situation (i.e., grain bed height exceeding its width) does not occur in a rectangular mash-lauter tun regardless of lauter design (e.g., false bottom, pipe manifold, or screen) or grist amount (e.g., high versus normal gravity recipe).
My personal observations with the high gravity brewdays seems to suggest slower lautering. But, there are too many other potential variables (different recipes, different wort temps, mill gap settings, coarse vs fine grist, use of wheat, etc.) involved in order for me to really be able to say for sure. So I certainly respect the views of those with far more experience. Nonetheless, being a practical person, I think the hypothetical 3-D MLT design isn't.