If I follow the question correctly - you need the full strength of the purlin in mid-span for reasons of stiffness against bending. The depth required at each bearing has more to do with absolute failure in shear.

Most timbers would have excessive flex or mid-span failure long before they break in shear at a tip - therefore the mid span needs more "meat" than the bearing at tenons or laps.

Oversimplified, but I hope it makes sense.

Pete