From what I know, most road frames are similar enough that stiffness doesn't have much of an effect on efficiency. The main exception is at the BB, where more flex could result in less power making it to the pedals. (There might be reasons other than frame flex that is shifting the tires, by the way.)

Not sure what you mean by "tire scrub," unless you mean "rolling resistance." I don't think increasing lateral stiffness will reduce rolling resistance; increasing vertical compliance might drop it a tad, but probably not by an appreciable amount in most circumstances.

And keep in mind that for many reasons, a stiff frame may merely feel like it's faster. A stiff frame will have a more lively feel; also, many geometry aspects that make a frame stiff will also make it handle more responsively, which again will feel faster (without actually being faster).

Unfortunately, it seems to me the only way you could really determine the performance effect of frame stiffness is to take two bikes with identical geometries, identical tires, identical rider position, identical power meters, and frames with different stiffness (but the same weight), and compare the efficiency of the two.

Until someone does that, I wouldn't worry too much about it unless you're in a highly competitive situation. Go with how the bike feels, rather than a parameter whose effect is difficult to quantify in the first place.