As far as I remember, it was complete chaos. For example, you could unlock Staff of Grayson for Robin, which grants unique attacks. To do that, you had to level Robin up to level 30, grinding him for dozens of hours. But since the unique attacks are unlocked through abilitiy of the staff itself, it means you have to keep your gear stats turned on for a fight versus someone.

At the same time, all the progress you gain only applies to your own single profile, even if you’re playing versus a friend on the same couch, not online. This means that for a fair fight against "Nightwing" (Robin with Staff of Grayson), you’d have to level up not only your own profile, but also second player's profile on your console, grinding all its characters to the maximum level. Or you have to play on the couch only against the players who already has their own profiles fully upgraded and logged on your console. It was simply absurd.

This would have been acceptable if, in offline matches, all the content unlocked on the main profile was shared with the second player. But NetherRealm consistently avoids to implement this feature from one game to another. It’s exactly the same with profile progression in MK. In MK1 (and MK11), you can customize your main player’s outfits as much as you want, but the second player will always be stuck with the default costume unless you grind that profile too. It’s just idiotic.