In my first attempt at this style bridge (camo version) I didn't have a sleeve and I found it difficult to keep my thermarest prolite in place on entry and while moving around. The sleeve could probably be replaced by a couple of straps to keep the mattress from twisting.
I'll also add that when the temps are cold the narrow prolite isn't wide enough to keep me warm. Anywhere my sides or arms touched the sides I froze. The cheap wide foam pad feels like the R-value is less, but it is wide enough it protected me.