And I have seen many court appointed lawyers show up not even knowing their clients name (but they did have it written down) and pleading them out immediately. I think they made a profit on the case.

Do you have any idea what they got paid? You can't think they made a profit if you don't know what they got paid or what their expenses are.

Here in NY we have a public defender where there are salaried attornies handling cases for the indigent. Some cases are assigned to assigned counsel when there is a conflict with the Public defender's office (for example when there are co-defendants who are both indigent). Assigned counsel are paid an hourly rate ($x for in court, $y for you out of court). These rates are nowhere near the typical hourly rates charged by even novice attorneys. Actually my firm charges more per hour for work done by a paralegal than these attorneys are paid.

Being that they are paid on an hourly rate, the fact that they resolve the case quickly does not guarantee much profit. Resolving a case quickly also does not mean that they do not do a good job. And not knowing their clients name is probably more a result of having getting files at the last minute.