Someone else already explained it in another comment (thank you!!), but all the "Dead Ends" are there for me to put a temporary stop to the storyline.
Some choices make it hard to connect one Day with another (such as when the player blocks or ignores Ren in Day 1; it wouldn't make sense to go on a date with him in Day 2). But for Day 4 specifically, it wouldn't make sense to have Angel stay anywhere near the ominous black smoke when even Ren seems aggravated by it.
I'd also like to clarify that the Dead Ends have nothing to do with [REDACTED]!