You can debate whether Han was in imminent danger or not (seems pretty clear to 99.9% of the populace though) but this is actually not the most significant aspect of the scene, dramatically speaking.
By having Han shoot first, you firmly establish for the audience that he is indeed a shady character on some level. He hangs around in hives of scum and villiany, and shoots people - justified or not. It's like in the old Westerns when guys would blow away each other over card games and think nothing of it. It just lets the audience know that with this guy, ANYTHING could happen. And our heroes (Luke, the droids, Obi-Wan) are hooked up with this guy. Are they going to be safe? Can this guy be trusted? It's an important tension and drama builder.
It also sets up Han Solo's all-important character arc - he goes from self-serving, ruthless smuggler only interested in money, to finding his "heart" and coming back to help Luke in the end. It's only because you're so firmly established in who he is, that his return at the end is a surprise.
These are time-honored, basic principles in dramatic storytelling, and that's all there is to it. By changing the dynamic, you remove the dangerous aspect of the character, and destroy his character arc. Drama 101.
_Mike