I noticed a big reduction in sparging/lautering times when I switched from my 10 gallon round Igloo cooler Mash Tun with a 12 inch SS Bazooka braid to a 20.5 gallon (82 Qt) rectangular cooler with the same 12 inch SS Bazooka braid. I do 10 gallon batches. I definitely agree that the grain bed height should not exceed the grain bed width or else you'll get significant grain bed compaction regardless of initial runoff speed--the result eventually becomes slow runoff speed and very long lautering times.
Take this into account when selecting your mash tun size and design. I highly recommend the rectangular cooler over the round cooler--It works for every batch size and gravity, and because the lautering times are consisistently short (I batch sparge), my brew day is shorter. There's no way I'm going back to the round cooler for a mash tun. I still use the round cooler for a HLT, though.