I agree that there are many different issues one could study in regards to latch-key children. Keeping the wonderful suggestions above, I would also suggest that you could examine different areas and the behaviors seen by the children located in these areas (rural and urban).
Another point you might want to include is the change of context. In the past there were many more kids left at home. Bow it seems that the world has changed very few kids are left at home. Is this due to a world that is worse? Or is this due to a greater sense of fear? Does the media have a role to play in creating fear? In particular, the role of perceived fear might be an interesting angle.
My experience was very similar to that of bullgatortail, except that it was my dad who passed away early. Being a latch-key kid can sometimes make you more appreciative of how hard your parent(s) work(s). Few people leave their kids at home simply to go out and enjoy themselves (at least this is what I would like to think).
Here are some links that may be helpful to you:
For an argumentative essay, you might want to argue for or against the idea of schools or community organizations developing after-school programs so latch-key children don't have to go home to empty houses. As a former director of such a program, I can attest that planned activities, shared with caring adults and other kids, can be a constructive and profitable way to fill the hours until parents are done working. There is lots of research to support the increase in juvenile delinquency episodes in the after-school hours - when latch-key children lacking in supervision may become involved in undesirable pursuits.
As a former latch-key child myself (my mother died when I was 14), I came home from school every day to an empty home where I was left to do my homework by myself or take part in outdoor activities. I made good grades and stayed out of trouble with the law, so I can attest that some children (especially teenagers) are capable of getting by for a few hours by themselves until the parent(s) gets home from work.
This is difficult because there are so many families who have both parents working just to make ends meet; they don't have much choice other than to trust their kids at home. It is difficult for single parents, too, not only because they don't have other adult helpers, but public school schedules are crazy sometimes. Just this week we had an early out day so we teachers could have meetings while the kids went home. Parents can't just get work off to attend to children who are sometimes out of school for irregular reasons. That's part of the reason I became a teacher; that is, so I could be off work when my little guy was out of school. It was difficult in the beginning, but now that he's older, he can work quietly in my classroom while I'm in meetings. It's certainly a tough discussion.
Some people argue that there is nothing wrong with the system of having latch-key children. They are only left to their own devices for a few hours, at which time they should be getting homework done. I knew many latch-key children when I grew up in a bedroom community. It can be very difficult on both ends.
One area that you could include in your essay is the the legal side of the issue. Research what the law says is the youngest age at which a child can be left alone without adult supervision. This law will likely vary from state to state and may even be different in each municipality. You could then do research on what qualities in a child should be considered before a parent would decide to allow them to be home along for any extended period of time. What do child psychologists say are the markers for that kind of maturity and responsibility?
There's been a lot of research done on this topic. Some people argue that having kids come home to empty houses tends to lead to them having problems with discipline and with feeling loved. It may also be a frightening experience for them if they are not old enough. Here is a link to get you started.