Several good reasons for removing the scene have already been mentioned above. Here are a few more:

This scene has become the first time that we see the Millenium Falcon. It ruins the "What a piece of junk" scene where the Falcon is revealed for the first time to Luke.

Jabba's apologetic attitude is contradictory to Greedo's behaviour. Greedo acted as if there was a price on Han's head. Jabba acted as if there wasn't much to it and Greedo was an idiot who just begged to be shot. This belittles both Greedo, Jabba and also Han in that shooting Greedo was not a big deal.

The Jabba of the original trilogy (as seen in ROTJ) would not allow Han to step on his tail and get away with it, would he?

Greedo has a twin? Triplets? It confuses the audience.

What the hell is Boba Fett doing here? And in armour with a ROTJ paint job? (He was not in the scene originally. He was inserted in the SE, and played by Mark Austin)

Is there anything in this scene's favour, you think? I can not see this scene as anything but redundant.

Gaffer Tape said:

However, I agree that it makes more sense that Han is simply hiding out on a planet far removed from the crime boss (planet that's the farthest from the bright center of the universe), and Greedo just happened to track him down.

Good point!

Btw. In the EU, Jabba's clan does not live much on Tatooine. He just inhabits the Bo'Marr monks' convent for a while (until the monks turn on the remaining entourage after Jabba's death).

Correction made in edit: The Boba Fett suit in ANH-SE was worn by Mark Austin, not Don Bies. Don Bies (great guy btw. I've met him in person. :D ) wore the suit in some shots inserted into the ROTJ-SE.