Why do chess tournaments award so many points for a draw? Nobody likes a draw. Why then do chess tournaments provide incentives for players to go for a draw by awarding significant points for a draw? Typically, a win is 1 point, a draw is 0.5 points for each player, and a loss is 0 points. So a draw is half of a win.

This is comparatively to other sports quite a large amount of points to get for a draw and essentially ends up encouraging players to play for a draw more often. Imagine you are rated 2500 and you are going up against a monster like Carlsen. Who in their right mind wouldn't want to just go for a draw and get a whole 0.5 points from that? 

In comparison, take other sports, like football, where a draw is 1 point and a win is 3 points. So the point system encourages one to go for a win. Similarly, many other sports simply don't allow draws and if a game ends in a draw, some sort of extra-time is played so that a winner is found (in Chess, I guess this could be arranged by having a quick blitz match best of 3 after a drawn game to decide a winner).

So why do chess tournaments give so many points for a draw? Wouldn't it be better to follow a different point system, like 3/1/0 as in football, to encourage players to go for a win?
I don't see how tournaments incentivize people to go for a draw. You literally cannot win any tournaments by drawing every game.
Yes sometimes there are draws that are clearly prearranged but other than that only bad players say draws are bad for chess. The funny thing is that these low rated players are usually not getting draws even against similar strength opposition. They also can't figure out what's going on in high rated games without an engine.
The issue being your football system is it would change the elo system and encourage win trading. The best way to gain elo would be win farming against much weaker opponents, as you would lose elo drawing against people of similar elo. The players with the highest elo would not be participating in these super tournaments to maintain their elo. Also colluding draws is nowhere near as damaging as win trading in this system, as the tournament winner cannot really win by drawing every game, but can easily win winning 50% and losing 50% of his games. Also it is freelo due to 1 win and 1 loss against a similar rated opponent being a net gain in elo.