Loser doesn't get his pick of stages in Soul Calibur, and that game's stages plays a huge role, Aeon in a small stage with ring-outs makes almost any match-up in his favor, yet put him in an endless stage, or a stage with walls and he is barely mid-tier. Same with Tekken, the loser of the first match, doesn't just get his free choice of levels.
It's a very viable tactics to go back to stage select and pray to the random gods that you get a stage in your favor, if you lost, but sometimes the random gods are evil and give you the exact same stage you were just on.
First stage selection should be completely random, and then if the loser wishes to attempt random luck again, he can either random it up or use the 50/50 coin flip. This is how it is in any competitive fighter where stages matter. I see no reason why Injustice is any different.
As for the interactables, no, they are not the same as random items falling from smash, they are part of the stage and can be trained on how to use and defend. It's no different than working on corner combo's, walled combos, ring out set-ups, or any other tactics involved with a particular stage.
Once again, I feel like the majority of the MK community doesn't know enough about other games or the tournament environment to make an objective decision.