In any democracy, most people ultimately vote on what's put in front of them by somebody else. It can just as well be "vague generalizations".
Brexit is not a failure of direct democracy.
Otherwise, if it's to survive, it does so by compromise, tradeoffs, bargaining, and leaving many people at least a little unhappy but not enough people unhappy enough to dismantle the system.
But in any case, in a direct democracy, if enough people want to vote on something, they can, regardless of how stupid it is. That would include Brexit etc.