As somebody that worked as a caseworker an innercity welfare and who had the richly earned streetname of The Devil Himself, the "Welfare Queen" sterotype was quite rare.
The typical client was between 18-35, had one-two child, and "Daddy" was gone. That probably counted for more than half of the clients. Many had disabilities and could not work (they would often apply for SSI).
There were a few "professional clients" and numerous clients who got jobs and didn't report it (we'd find out through IRS records). Here, we are talking about very low paying jobs that made them ineligible for cash. This might, all things considered, have accounted for 10% of the recipients.
One client I interviewed was convicted of defrauding the state of over $100,000 by faking the custody of her children. So it does happen.
I think you summarized the situations rather well.
Now, I know of people who would like to work, but have children, and the rules are such that if they were to work, their childrene would lose benefits which would not be replacable dollar for dollar by earned income.
One part of reasonable reform is to avoid making people worse off if they do work.