Because you're not optimizing for the success of the law firms or their clients, but for the structure and integrity of the court system. That integrity depends heavily on the fact that lawyers are trusted repeat players who have a lot of exposure and are personally on the hook for any problem. (Moreover, because a law license is not a right, the due process requirements and burden of proof for disciplining lawyers is far lower than for imposing criminal penalties on non-lawyer individuals. You don't need a trial, you don't get a jury, there is no "beyond a reasonable doubt." Supervising lawyers can be held liable for the misconduct of their subordinates with little showing of knowledge or intent regarding the misconduct.)

"Better" is a value judgement, and the specific value you've chosen is "makes more money". One concern, I think, is that a non-lawyer may push employees towards legally-unethical behavior. Since the non-lawyer can fire the lawyers, that gives them a big stick they can use to influence the employees.

Lawyers are subject to ethical requirements that are not imposed on non-lawyers. And those ethical requirements are just that - requirements. If a lawyer breaks them, they jeopardize their entire careers. There's no equivalent for a professional CEO. Clients insist that their attorneys act in a fiduciary capacity.

This is very different from the chip engineer scenario. It is the most important reason why non-lawyers are not allowed to own law firms. Because non-lawyers are not bound by rules that require them to put profit motives second in many circumstances.