Will's post nailed the reasons. But I think there is another group who play, guys with virtually no chance of winning, but simply enjoy the feeling that you get in a medal play tournament. I was always a good match player, but TERRIBLE in the stoke play qualifying for our club championship. So I started signing up for mid-am qualifiers to get better at stroke play. It took me four times before I made a cut, but my club championship qualifying scores got much better.
I also think there are many amateurs who did not play competitive golf in high school and college, maybe they played other sports, or maybe that just became decent at golf later in life (I am in this group.) Amateur tournaments are a great way to test your game, and the mental challenge of managing your score for the whole round is FAR nore difficult than match play. In fact, it is an element of the game that very few amateurs experience. Imagine if there was a stroke play event for 16-20 handicaps. Imagine those guys having to finish each bad hole, no more triple bogey max, or picking up and saying: "your hole, partner."
For competitive people, amateurs tourneys are a perfect barometer to measure your game under stress. So while my record is nothing to brag about (one mid-am qualified, one MGA senior open cut made, 6th in the NJ pre-senior am,) those rounds represent some of my proudest personal accomplishments in golf.