Why Replay Reviews don't Work in Baseball

I was watching the Jets at Redskins game yesterday when the following scenario played out. If I remember correctly, Rex Grossman handed the ball off to the running back. The defensive players made contact with the Skins running back which caused a "fumble." The ball came out and as the defender was picking up the ball in an attempt to take it in for a touchdown, the ref blows the play dead.

Why? If the ball ever comes out during contact, whether the player is down or not, why blow the whistle? It seems like the ref just took away a possible defensive touchdown.

Not only is a defensive touchdown out of the question, now the defense must utilize a challenge to prove that a fumble occurred and the play should result in a turnover. Once again, Why? Shouldn't the burden of proof be on the offense since the player failed to safely secure the ball as he's being brought to the ground?

I think the defense should automatically assume possession if the ball comes out at any point during the tackle and the offense should have to use a challenge flag in order to resume possession. 

This is exactly why replay would not benefit Major League Baseball in any way. First of all, we would be making a long game potentially longer. Imagine watching the Orioles in replay... I wonder how long the game durations be. I don't think I want to know. The nature of the sport does not allow replay. Example, what if the batter hits a fair ball but the umpire incorrectly calls it foul? The manager challenges the call and it is overturned. How many bases is the batter awarded? By all means, correct me if you believe my logic is flawed.