One additional point - feedback from beta testers often has a significant impact on how a game is fleshed out during development. During beta, the entire game is undergoing massive changes as they try to determine what gameplay works and what doesn't, and the input from people playing it is likely to affect the final form the game takes. Consequently, some people enjoy trying to nudge the game's development in the direction they feel it should go, and betas offer them that opportunity.
By the time the release rolls around, the game is pretty much settled into its final form, and only minor changes will be made after that via patches.
| it's like making people pay to do the testing for you |
1) No one's being made to do anything.
2) No one's paying to beta test. The game is the same price whether you buy it now or you buy it in February. The people that choose to beta test haven't paid a penny extra, they're just promising to buy the game when it's released.