The more you have to correct for buildings "falling over," the more you source data you lose from having to stretch a portion of your source file. The shift function can eliminate or minimize that effect and can help maximize the number of pixels you have on your "subject." With a normal lens, you might have to change the angle to keep the subject vertical lines vertical, which might give you too much background/foreground that has to be cropped out.All well said.
Tilting the focal plane is not something that can be done in PP. You can't make an OOF area more in focus. Let's say you take a picture of a deck or sidewalk from where you are on the ground to the horizon. A regular lens will have a portion of it OOF closest to the camera because of its DOF even if shooting at f/11 or smaller. With a TS lens, you can shift the focal plane so that it is parallel to the deck/sidewalk and still shoot at f/4 (max aperture). The sidewalk with lay completely within the focal plane even though the DOF is thin, but the DOF effect can't be seen because there isn't anything on top of the deck/sidewalk.