I believe it is called contemporary style and it is useful for putting windows or vents on the vertical. A single pitched shed roof would be simpler and less expensive, but maybe he just likes the contemporary look better. Its just to do this, your way is one way, but he will need a 2x10 joist has the joist will have to support the whole roof. The rafters will not support each other like they do in a normal roof.

Here is an alternative, use an LVL, or three 2x10's nailed together as a ridge beam. Eliminate the joists. Use 2x6 rafters on the back side resting on the back wall and hung on the ridge beam. A second ridge beam under the first made up of three 2x6's would support the front rafters. The space between the ridge beams could house windows and/or vents (crank out windows hinged at the top?).

I think this would work with a little more roof pitch, 4/12 isn't going to leave much room.