Matt:
What you seem to be talking about is what we would call the floor of the bunker.
Yes, the floor is part of the design. Some are intended to be flat . . . Macdonald and Rayner put cinders on the floors of their bunkers, and when we dig them up to rebuild the bunker now, we can see they were built flat. MacKenzie and George Thomas and others went for a more concave shape, although in general I believe the outside edges and lips are now higher and therefore the faces are steeper than they were when they were built. [It's hard to tell from digging them up, if there isn't a heavier soil underneath.]
Many bunkers that started flat wind up edging the bunker higher and adding a bit of upslope at the edges of the floor, to prevent difficult lies. Nearly all pot bunkers have a bit of slope there, so you aren't right up against the wall.
The nastiest thing you can possibly do is shape the floor so you have a slightly downhill lie as you play toward the green. Jack Nicklaus did that at Muirfield Village for a little while . . . I only know that because I heard the players complaining about it in private.