Anyone have any idea why draws are worth 1 point rather than 1.5 points?
1.5 points? Decimals in the points system?! Your question is more appropriately phrased as why is a win worth 3 instead of 2 points. With all due respect then, I'm guessing you're quite young. It used to be 2 points for a win. It was changed to 3 points for a win from the 1980/81 season on. It was then adopted for international tournaments from the 1984 Euros Final tournament.
The trouble with 2 points for a win is that teams who were drawing were not necessarily given sufficient incentive to risk their point and go for the win. With both teams not necessarily seeing sufficient reward for risking their point, games that were being drawn late on could become low in action.
3 points for a win means you can gain 2 by only risking 1, so teams are more likely to go for it. The system doesn't necessarily reduce draws, but it does tend to mean teams are more likely to be attack-minded late in matches.