There may be other states that have an initiative process. Oregon does I believe. Any person in California can propose a law given enough signatures, and every eligible voter gets to vote on that law. That sounds pretty close to direct democracy to me.
Direct democracy is often used to describe the Athenian democratic model, and in Athens only a certain portion of the populace was accorded a vote. In the end, direct democracy is what led to Athens' downfall.
Please don't quote me BP, because I could be wrong or have some specifics wrong, but the way I understand it
I think there are obvious problems, if not only logistically, of allowing a direct democracy in trying to manage what is voted on and who is eligible to vote. I was taught that in a direct democracy, all it took was an interest in voting on whatever, through whatever means, became a recognized votable issue and then exercising that vote. I wouldn't describe only a portion of any populace being accorded a vote as being "democratic" since even before the voting starts, a portion of the populace has already been excluded. I could be wrong.
In addition, there has to be some means to determine whether an issue rises to the level of a need (and cost) for a statewide or nationwide referendum where such would be provided for. A petition with w minimum amount of signatures of some form of vote to determine whether to vote on an issue is done. It's not like anyone of us going up to the capitol building and saying to whatever powers that be, that we wish to have a statewide vote on an issue that's been on our mind and our wish becomes their command. For logistics alone, there has to be some level of criteria that is met even to trigger a vote on whether to vote on an issue.
The downfall of the use of a direct democracy should be easy to see, especially where populations grow to numbers much larger. There are places in this country where direct democracy processes and mechanics can still work, but at much lower levels of government, mostly or all local. A community of 700 people likely does not need a full blown representaive government on the scale of state and federal governments, logistically it is easier to hear all those that want to participate and to vote on at least some local issues rather than have a city council or a village board of selectmen make all or most of the decisons. Town Meeting Days all over New England are about as close to a direct democracy as one might get in this nation, but they only work because of and under certain limited circumstances.
Great Britain even saw a need for change from a monarchy to a more democratic form of government and an eventual form of an indirect representative democracy. It still survives as a nation, even if just a shadow of the size of its once geographic dominion. Logistically it recognized, before it was too late that logistically, the further a dominion became spred, the thinner the cover of that spread and eventually holding the spread in place would become overwhelming and destructive to its survival. The same with other surviving nations who also at one time in history, represented much larger geographical empires.
I wouldn't prefer a direct democracy on a scale any larger than several thousand people at most, simply because of the logisitics and cost for administering a vote every time a petition met the criteria for calling a vote on a vote or a direct vote in the issue. If a state has a propensity to solving issues through statewide referedums and proposals, it make it hard to do much of anything without using that method and if it grows as a means to decide legislation then it will eventually bog down and overwhelm any indirect and representative democratic means for determining legislation. I don't know for sure, but I think most, perhaps all states have a provision for their residents to bring a referendum forward by petition to those that receive such petitions and there is little choice to refuse a petition properly executed.