Fatalities were originally an attempt to make the stun mechanic in Street Fighter 2 less punishing for the receiving player by leaving it as a finisher.
A quote from Ed Boon, the co-creator of Mortal Kombat:
"One of the things about Street Fighter that annoyed me, and I loved, was when you get the other guy dizzy.
"That was such a bad feeling, and it was such a good feeling when you're the guy attacking them.
"I want to have that good feeling, but I don't want to give the other guy the bad feeling.
"So we moved the dizzy to the end of the fight."
As a result, Mortal Kombat allowed players to perform a devastating final blow on their opponent, but only when they had already lost, instead of diluting their chance to win even more.
Source: How Street Fighter II Inspired Mortal Kombat's Fatalities - IGN Unfiltered - https://www.youtube.com/watch?v=K9cx6GqvJLg