There are multiple facets to this question depending on the type of law you are talking about.

Criminal, Civil, Contract, Torts, Family, etc.

In many areas of law I would agree with your statement, however with criminal law I have always felt that many governments have been in the habit of criminalizing poverty in many ways. Personally I think it should be mandated that at a minimum for every $1 given to a prosecutor's office to prosecute criminal cases, $0.50 should be given to public defenders (ideally $1 for $1 but I would take $0.50) currently is more like $0.10.

Can it be a socio-economic problem? Do universities that these lawyers study at really need to be as expensive as they are?

Education is always expensive, in every country, because it takes time. US-Universities are just exceptional expensive for whatever reasons. But time is something that this technology can remove for this cases, so I would say it still remains an economical problem.

Though, the ability to use the technology might come down to a social problem. Because it still needs a certain level of education and competence to use the technology. Just significant less than visiting a university for a whole decade or so.

> So it's an economical problem, something the state can't easily solve.

The state can simplify the law and eliminate or stop prosecuting laws that don't directly harm people, thus reducing the demand for lawyers. It's not just an economical problem.