A-frame really
doesn't use meaningfully less lumber than a box style for the same footprint (and
not all its footprint is totally *usable by chickens*)... unless you insist on having the tractor be walk-in height, in which case yes an A-frame uses *slightly* (not much) less material than an equivalent height box.
The way the sides angle down in an A-frame style means that a chicken can't stand fully erect along the edges of the run and house; and in very low A-frame tractors they often can only use those edges "under the eaves" in a sitting or bending position. So the floorspace is not, from a chicken standpoint, quite what it measures out at.
Also, unless you have a really miniscule house portion (that does not use the whole length of the coop), you are stuck with a popdoor in the floor, which involves many inconveniences.
Finally, and here is the biggest problem with an A-frame, you are
stuck with a very small house portion. There is just no way to make it more ample; and unless the A-frame is narrowish and walk-in height, not all of that space is usable anyhow. Furthermore it is an extra-small air *volume*, making it even
harder to adequately ventilate in wintertime than your average small coop.
In favor of an A-frame, they are a bit less tippy in high winds than an equivalent-height-and-footprint box style coop. And of course they look kind of Swiss chalet cool.
It is not that I am against A-frames, as such. They can work just fine in year-round mild climates where the chickens are allowed to free range most of the time -- and notice that this is basically the situation they were designed for, i.e. British backyard chickenkeeping
But in any other situation, they have so many really significant disadvantages (for the chickens, and for easy management) that a rectangular, box-style coop would really make a lot more sense.
JMHO,
Pat