How well do mechanical (non-hydraulic) disc brakes generally function when used with brifters?-- This combination seems to be increasingly common among e.g. adventure bikes such as the Salsa Vaya, Genesis Croix de Fer 10 and Specialized AWOL) as well as cyclocross bikes (e.g. the Fuji Cross 1.1 and Merida Cyclo Cross 300) but I was told during a custom-bike consultation at a LBS that current non-hydraulic disc brake technology is not mature enough to work well with brifters: Apparently it has something to do with the difference in mechanical advantage between road bike- and mountain bike-style brake levers. Is this information true?-- if so, is this combination just a marketing gimmick?
As other have stated road discs are becoming more common. While hydraulic discs will give you the best performance, it comes at considerable cost. New shifters would be needed. Mechanical disc would reuse your shifters. I would put mechanical disc as a cost effective alternative. If this is an upgrade it is important to use road specific calipers. Mountain calipers and road calipers have a similar appearance but are not interchangeable.
They function fine. Cyclocross bikes with mechanical discs wired to brifters are a common sight in races.
However, mechanical disc brakes are in fact inferior to hydraulic disc systems and I wouldn't recommend buying a new bike with a mechanical disc setup when there are so many good hydraulic options out there.
Mechanical disc calipers only move to squeeze the rotor from one side, leading to uneven pad wear. They also have less power at the lever than a hydraulic system, which it seems like you may be concerned about. In a hydraulic system there is virtually no friction as it is all fluid, and no cable stretch or breakage.
The only reason I would personally have for a mechanical system, and I think it's a valid one, is that the shape of hydraulic brifter hoods is very different from their mechanical counterparts within the same brand family. Usually the hydraulic hoods are taller and more robust, which can be good for people with large hands, or uncomfortable for others.