If we do this, we'd be lead by whatever accidental majority gets in. And they have no incentive to do what the people want. The only saving grace would be that people have more of a sense of duty, and thus are less likely to abuse their power. But beyond that any unlucky draw could really screw over a country.
What greater incentive do current voters have for picking the correct policy/representative? Either way, people with power are balancing their personal interest with justice / the public interest.
Voters don't, but politicians have incentive to listen to voters, rather than being totally in it for themselves.
In other words, the desire to be re-elected causes politicians to listen to the people, rather than do whatever they want. At least, that is the theory.