The problem is that they tend to have dimensions that almost match. If I make a wall of bricks, and put a single off-brand brick in it, then suddenly the wall isn't fitting together anymore properly because of that mismatched size. The same goes for all kinds of more complicated constructions.

They're compatible enough so that they can be connected with lego pieces, but incompatible enough so that they shouldn't be connected with lego pieces. So we keep all the off-brand bricks in a separate boxes to avoid intermixing; you make a whole thingy only from lego bricks and a different thingy only from not-lego bricks.