I played the DLC and I must say, the alternate reality Rapture City surpass Columbia. They brought back the survival horror feeling from the first bioshock and perfected the leveldesign.
The way they link Columbia to Rapture is about the chicken and the egg problem. Which one came first? With multiple universes that do not share a single timeline it's impossible to know. That literally creates an infinite loop with no beginning or end. That's why I think bioshock 4 would have a hard time sticking to the infinite's multiverse. It can be a universe in its own, but at the same time I'd be bound to Elizabeth's timeline in one way or another. The easiest solution is just to leave Elizabeth behind.
Elizabeth's power was wasted on infinite. In Max Payne 2 there were levels that you would see the same plot from Mona's perspective. They lost the window to explore Elizabeth in more creative ways, such as using alternate realities to bypass security for instance. They nearly did that in the DLC when Eliabeth opens up a tear for you to grab the winter plasmid from another reality.