The basic problem of direct democracy is one of bandwidth: how can an ordinary citizen afford the time to become properly informed about the decisions they are being asked to vote on?
Modern society is extremely complex, and many of the everyday problems are ones of management and compromise. Arguably the best people to deal with these questions are those who are expert in them.
To take a simple example, suppose you were asked whether the people in charge of your water supply should spend $20M reducing leaks in your regional water network, or whether it would be better to spend the same amount of money on repairing old sewers? Merely to have an intelligent opinion on the question would involve some hours of study. Now multiply that by all of the thousands of technocratic decisions that must be taken every year to keep society running effectively. Clearly, government is a full time job.
Worse yet, as the population increases, so the "reward" of direct influence on the decision making process becomes diluted. What is the point of spending hours educating yourself about water supply and sewage disposal if your input is reduced to one vote amongst millions? You vote Yes, 55% of the population vote No, and that's your weekend's studying wasted.
But on the other hand simply appointing a technocracy and leaving them to it doesn't work either: the technocracy just becomes a self-serving oligarchy.
One approach which has been suggested, and even tried on a limited scale, is Citizens' Juries. The idea is to take a randomly selected group of voters (typically 20 - 30) and provide them with the time and resources to get really educated about a topic. This includes witnesses and experts who can provide the necessary background information and answer questions. The rest of the population can then be reasonably confident that they would have reached similar conclusions if they were to take the time too, and hence the findings of the Jury have democratic legitimacy. At the same time the demands on the time of the jurors are sufficiently limited to be manageable.