In arcade mode for UMK3, if you win every match against the CPU without losing, you won't go through enough levels to see the old stages because they have a very strange repeated order. Basically, if you play on Double Master the last stage against Endurance should be the Subway if the first stage was Lost, but in vs mode, it's more likely you'll see them due to longer runs without restarting the game. Rest assured, they do show up in a very specific, but finagled order. In the hacked TE version of UMK3, the stage order bugs have been fixed.
In MK3, the stage looping happens on the uppercuts through levels on the balcony to the street, and when the game sees it's on the street it goes back to the next stage, rather than advancing to the stage after the balcony if there were no uppercuts through.
I think I explained that right,
@Konqrr anything to add?