Although you make a valid point, I wouldn't be so quick to dismiss those who are self-employed as being unemployed.
Certainly, some of them fall into a very undesireable state. They have huge student loans to deal with and they have very little income. Maybe they're picking up a court appointment here or there for very little money, whatever.
You can see how a person like this could muddle along, but eventually make enough money to rent an inexpensive office space. Then, maybe a slightly bigger one where they share a receptionist with a few other solos, etc. Working their way up the food chain, until they build up an individual practice and manage to accumulate a few real, paying clients.
Especially for the grads who are 20-something, you're going to live a LONG time. Taking 10 years to go worse than minimum wage employment, to the point where you are billing 30 hours a week at $150 an hour seems like a very long and hard road. However, the folks who do it will eventually end up making a very, very good living.
Granted, it's probably not what they envisioned when they started law school, but it can happen.