SWE to lawyer here.
The analogs of the traditional coding interview in the law school world are the LSAT and classroom timed memory tests. Both have absolutely nothing whatsoever to do with being a lawyer or the kinds of activities that lawyers actually do.
What they are are intelligence tests. They are easy ways for judges and top tier law firms to tell if you are "one of them." You can get your foot in the door if you can perform, at a minimum, at a certain level. There are plenty of things you can do without 97+ percentile LSAT and A's in law school, but you are screened from the top echelon of work.
People object that this isn't fair and screens good people out -- false negatives. But experience has shown that it is effective and easy. Perhaps there is a better way, but this way seems to work well enough. There is little incentive, beyond some people complaining about it, to change a system that is working well.
I see the traditional leetcode interview in the same light. The point is to see if you can perform at a certain minimal level. Yes, it's arbitrary, and often unconnected to real life. But it is an effective way to gauge a minimum level of intelligence and competence. Not perfect, but easy and effective.
Finally, there is ego element to this. People who can perform at this level see these skills as a minimum qualification. They are uncomfortable seeing themselves in relation to others who cannot perform at this level. Knowing that their peers have similar minimum qualifications makes them feel safe and secure about their status. This is not a criticism, just an observation about human nature. People in a club need a shared identity.