So, machine learning does get used quite a bit in the legal industry, at least outside of small practice. But it tends to be much more successful when it's used as a force multiplier for humans rather than a replacement for humans.
For example, the idea of using document classification to reduce review costs has been around for a long time. But it took a long time to get any traction. Some of that was about familiarity, but a lot of it was about the original systems being designed to solve the wrong problem. The first products were designed to treat the job as a fairly straightforward binary classification problem. They generally accomplished that task very well. The problem was you had to have a serious case of techie tunnel vision to ever think that legal document classification was just a straightforward binary classification problem in the first place.
Nowadays there are newer versions of the technology that were designed by people with a more intimate understanding of the full business context of large-scale litigation, and consequently are solving a radically reframed version of the problem. They are seeing much more traction.
The coordination problems in creating a system designed from the beginning to be human in the loop is a challenge.
There are a lot of great ML algorithms, even if you limit yourself to 10-20 year old ones, that aren't leveraged anywhere like how they could be because very few know how to build such a system by turning business problems into ML problems and training users to work effectively alongside the algorithm.
CRUD application development projects blow past deadlines and budgets frequently enough. ML projects have even greater risks.
Edit: I hope the people making the successful legal document management system you mentioned write about their experience.
FWIW, my experience has been that, if you're trying to build a system that works in tight coordination with humans, you're better off sticking to algorithms that are 40-80 years old. Save some energy for dealing with the part that's actually hard.
For example, the idea of using document classification to reduce review costs has been around for a long time. But it took a long time to get any traction. Some of that was about familiarity, but a lot of it was about the original systems being designed to solve the wrong problem. The first products were designed to treat the job as a fairly straightforward binary classification problem. They generally accomplished that task very well. The problem was you had to have a serious case of techie tunnel vision to ever think that legal document classification was just a straightforward binary classification problem in the first place.
Nowadays there are newer versions of the technology that were designed by people with a more intimate understanding of the full business context of large-scale litigation, and consequently are solving a radically reframed version of the problem. They are seeing much more traction.