Forgive me if I'm wrong, but it looks like a lot of the champions you listed are poke champions that rely on a level 6 burst to all in.
On top of that, you aren't even certain with three of them.
You are right, Azir can also farm with soldiers, but he can hold onto a soldier, use Q to reposition soldiers, and ward to prevent being ganked. On top of that, if we're waiting till 6 to all in, he has his wall. His dash can take him over the walls in river, I've watched it happen. So unless he's paying no attention at all, not warding, and using all of his skills haphazardly, he still holds the chance of getting away... Without flash. A pretty reliable chance actually.
You are arguing that he is playing like shit, and I'm arguing he's playing perfectly, so let's assume it's somewhere in between. Let's say he's at the tower, has a trinket ward down, and because he's at your tower, he's smart enough to hold onto one charge of his soldiers because he is overextending and the jungler may show up. He can still get away unless his lane opponent or the jungler land a series of CC against him. He has his E, his wall, and flash. Granted, flash being down is a successful gank.
I'm sure he's vulnerable before he picks up his dash, but if he's pushing that early, he's probably going to lose more fights than he wins unless his lane opponent is horrible, but I also don't believe the champions you listed at level 2 can all in him, but I've been wrong before.