Set points also don't work when you choose your opponents. Why risk taking on the #1 player in the league when you can take on the #50 or #100 player in the league, at a much lower risk and the same reward? At least with Elo, there are the higher ranked players, who if you beat you get more points, but if you lose to, you lose less points, and vice versa, so that the risk is proportional to the reward. Low risk of losing and low ratings gain potential but high ratings loss if you play against a lower ranked player, and higher risk of losing and higher ratings gain potential, but lower ratings loss if you lose against a higher ranked player.
Set points would only work in events where everyone plays the same number of games with each other. To take the soccer analogy further, in the opening groups of the World Cup, four teams square off against each other, and they all play each other once, with 3 points for a win, 1 for a tie, and 0 for a loss. This works because they all play an equal number of games. If, for example, Canada and the USA each play 1000 games against each other and go 900-100, and Germany and Brazil go against each other 10 times and go 5-5, then Canada has 2700 points and the USA has 300 points, and Germany and Brazil will each have 15 points. That's... not fair :p Someone with a 10% win rate would thus outrank someone with a 50% win, and they would do it losing to a worse team.