Yes it does, just elsewhere. For instance, the driveshaft u joints, and how far it pulls the spindle out. It also affects spring and strut travel if they don't have a similar lift. It also drops things, which decreases ground clearance. In the case of the Ascent, a 1" drop keeps the rear differential above the bottom of the car, barely.Something that you kind of touched on here is there's a big difference between a suspension lift and a body lift. A poorly done suspension lift will affect steering geometry, wheel alignment, and suspension travel. A body lift (as is done with spacers) doesn't do anything to the suspension.
Also, a subframe lift makes it a lot easier for the subframe to move, wrecking all sorts of things. It's why I designed and built my own.