One thing to keep in mind is that not all situations require 2 perfectly flat and coplanar faces. A small variation in thickness may not be noticeable. For example, the underside of a bookshelf. Also, the exact thickness of a piece is not always critical; it’s probably not going to be noticeable if that same bookshelf is 3/4″, 23/32″, or even 11/16″, as you should mate the individual dados to the individual shelf pieces anyway.
Also, using a smaller plane (#4 or #5) and focusing on the high spots alone while checking for twist is a good path, as noted by others here.