“It ensures that your legal work is done by professionals who have spent years to study the subject. The costs to making mistakes in this industry are high and we choose to maintain a high standard of quality by ensuring legal subjects are only handled by professionals with requisite experience”

Essentially, think of anyone who argues for certification.

That's fair. So this is just partnerships, then? Is a lawyer still allowed to take part in leadership of a company that has non-lawyer leadership provided it's not a partnership, specifically?

Law firms are typically structured as partnerships. I'm not sure if that's because there's another restriction against operating a law firm as a non-partnership or what.

If a lawyer was part of a company that wasn't a law firm, that would be fine. Actually, this happens pretty frequently--many sports agents happen to be lawyers, because sports agents are responsible for contract negotiations and legal skills are valuable in that situation--though they do not necessarily represent their clients as lawyers and hence the sports agencies they own and operate aren't treated as law firms.

For example, Drew Rosenhaus is a lawyer and a prominent sports agent, and his firm is neither a partnership nor a law firm. Rosenhaus is famous for a number of things, such as being the real-life inspiration for the title character in the film Jerry Maguire and holding a press conference with his famously difficult client Terrell Owens during one of the many controversial incidents he got himself into and responding to every question from the reporters with the phrase, "next question". He was also the agent of Chad Johnson, who famously legally changed his name to Chad Ochocinco for four years to get around league rules preventing him from putting that inaccurate Spanish translation of his jersey number on his jersey in place of his surname.