Sounds like a really interesting concept at first, but when I think about it a bit more I think its kind of stupid for several reasons.
One of them would be collution.
People would be apt to collude in those games, and if you do win the 2000$ jackpot, the poker site
would probably start some kind of investigation against you to see if you colluded or not.
And since SnG's usually have a lot of regs they would probably find something if they looked hard enough, no matter if you cheated or not.
They could say something like, this and that player played in all 4 games against you, and it appears they played a bit more soft vs you.
Another reason is playing scared money.
Lets say you have already managed to win 3, and its going very well in #4. You will then probably be very nervous, and that might affect your game in a negative way.
A 3rd reason is that it adds to the variance.
If you are a slight winner normaly you would be an expected slight loser in these games, provided you dont get the jackpot.
So it will become more of a lottery really.