Aside from the seat tube, there is no possible reason for having "single-butted" tubing on a frame; not for weight, strength, or cost. The tubes are either butted at both ends (occasionally to different gauges, where those would be called TRIPLE-butted), or not at all, which would be called STRAIGHT gauge. Butting only 1 end, and leaving the other end thin would cause incredible weakness at that end.

I think the OP is unclear on the subject, and is just picking up that theoretically, triple-butting costs more than double-butting, ergo, there must also be a non-existent "single-butting". I would suggest a quick Wikipedia search on the terms "swaging" and "butting" of tubes.