But in practice they aren't. In practice a represntative is swayed by people with money to go against the people they represent.

There would be little to no opportunity for that in a direct democracy. Lobbyists can't bribe everyone, it wouldn't be cost effective. Meanwhile people will have no choice but to educate themselves, as they'll feel the effects of their votes directly and won't be able to hide behind the (sometime inevitable) betrayal of the person they voted for. Even if people are lied to and convinced to vote another way, there's a huge difference between "You lied to me and didn't do what you said you'd do" and "You lied to me and got me to do something I didn't want to do", and generally there should be more accountability.