Most states enacted their professional responsibility rules similar to the ABA model rules. New York and several other states have different rules. For example, New York has its own model code of professional responsibility. The rule of not to partner and share profit with a lay person has been in the ABA model rules since day one. Minority rules are similar at this point. I am not aware in any state that a law firm or a group of attorneys can be controlled by a lay person. They can form a partnership selling ice creams together. Just not practice law.
On the other hand, state laws vary regarding whether a lay person can practice law. Most states outlaw an unlicensed practice are different in punishment. In California, for example, a lay person practice law would be a misdemeanor. For example, Calfornia allows trial by written declaration to fight traffic tickets. There are some well known websites to help people write such a declaration. In my opinion this walks on a very thin line of unlawful practice because such a declaration not only includes a statement of facts but often includes some defenses. How to choose a defense requires legal judgment, which can only be done by an attorney licensed in California. A DA would hesitate to prosecute for First Amendment concerns but it does not mean such a layperson practice is legal.
The reason for ABA to enact Model Rule 5.4 is to protect the professionalism of the legal practice, and to protect the consumers as well.