Accounting firms used to have the same rule (though they've relaxed it a bit to allow non-CPAs to own less than 40% or 50% as the accounting firms got more and more into "consulting"). The rationale is explained well here[1]. Large law firms are making a similar, though slower, transition to expanding their consulting services. Particularly with respect to data privacy and cybersecurity. I would expect the rules to relax over time.
The U.K. recently permitted non-lawyers to invest in law firms but it doesn't seem many investors have jumped in head-first. Law firms and accounting firms don't have much by way of "assets" so they can be quite risky. I briefly worked at Deloitte with a former Arthur Anderson partner. He was quick to warn all of the young staff about what a terrible investment his equity had been. One rogue partner can sink the entire ship and leave the rest without much ability to recoup the money they put in.
Just seems like an excuse to maintain a racket to me.