Tyre shape and rolling resistance
 

In line with the information here:
http://www.atob.org.uk/technical/small-tyre-design/

wouldn't it be the case that a tyre with a flatter central section will deform less under load and therefore roll better? I'm wondering why a tyre like a Big Apple has such a rounded profile compared to e.g. a BMX tyre like a Maxxis Grifter.

That article kinda read like a Greenspeed ad. Wonder how well the Schwalbe Kojack would do in their comparo?

BA's and Grifters have a different profile because they're designed for completely different riding. The BA is designed for normal riding. The Grifter is designed for banging off things and landing from decent heights. A squared tire would provide a greater contact patch when hitting a curb or landing from a jump.

What hurts for rolling resistance is how much energy is lost when the tire deforms. If you had a tire with very thin rubber and extremely flexible sidewalls then it would still deform by a considerable amount, but there would be very little energy loss due to the tire's flexibility. That's the nice thing about having flexible air-filled tires - they can deform to cushion road shocks, but the resistive force from the front part of the contact patch where the tire is being compressed is almost all paid back by the pushing force on the rear part of the contact patch where the tire is re-expanding. The Grifter tire with a somewhat squared-off profile isn't going to be as flexible since the rubber at the edges of the tread needs to be thicker to give it that profile. In addition, that tire has a less efficient tread pattern, with deeper cuts in the surface and far more of them. All the individual blocks of rubber in the tread will squirm around in the vicinity of the contact patch - at a cost of some lost energy. For minimum rolling resistance you want minimal tread pattern - a slick tire or something close to it.