The legal field isn't really amenable to simplistic economic analysis. With all due respect to thinkcomp, the idea that licensing requirements are what is driving the cost of legal services is totally wrong.
First, legal services generally aren't that expensive. If you need someone to help you draft a deed to some property, you can probably get that work done for cheaper than you would pay an engineer to design you a retaining wall on that property. When people say legal services are expensive, what they mean is that high-end corporate legal services are expensive.
Second, corporate legal services is not expensive because of limited supply. There are about 45,000 JD's graduated each year, and maybe 3,000-4,000 are hired at big firms that do corporate work. The rest work for far less money, in the $45-$60k range. If you wanted to start a firm doing corporate legal services at low cost, paying attorneys $80k a year (half the going rate of a first year at a large firm), you would literally drown in job applications. While in a platonic sense there is a supply constraint in the legal field, it has a practical effect more akin to crash safety regulations in cars than something that actually constrains supply to drive up prices.
If the state bars got rid of the requirement that lawyers attend an accredited law school, there would be almost no change in the cost of legal services at the top. Big firms hire the large majority of their associates from only 20 or so schools, out of the 200 that exist. Why would adding a category of potential hires below the huge group of people already not getting hired drive down salaries?
The price of high-end legal services is insensitive to the supply of lawyers for the same reason the price of Apple products is largely insensitive to the number of Korean competitors in the market: 1) brand is tremendously important; and 2) there are actual differences in the quality of the product.
Re: 1) Because it is difficult to tell whether your lawyer did a bad job or whether you just had a bad case, branding and signaling becomes tremendously important. It is that branding and signaling that makes companies keep going to firms that hire primarily from the top schools, even when there is nothing, legally, that prevents them from taking it to firms that have more diverse hiring standards.
Re: 2) The adversarial nature of law means that there is an arms race for the smartest people. While a lot of even high-end legal work can be very routine and boring, some of it can be very complex. That 10% of legal work that requires out-thinking the opposing counsel can have major repercussions for companies, and as such companies are willing to spend the money to ensure that their lawyers are smarter (at least on paper) than the opposing party's lawyers.