Nothing stops the owner of a brokerage from selling. "Producing broker" and "non-producing broker" are market terms describing whether the broker still does personal deals, and they carry no legal meaning on their own. The term that does carry meaning is designated broker, also called broker of record or principal broker depending on the state. That's the one licensed broker who is legally responsible for the firm's compliance and for supervising its agents, and the requirements for that role, including whether one person can hold it at two firms, are set state by state. I haven't seen a state that bans that person from having their own clients, but supervision duties are real and you'd want to confirm your own state's rules with the commission or a license attorney before you plan around it.
The competition worry is about lead flow, not law. If your firm generates inbound leads and you route the good ones to yourself, agents notice within a month. Firms that produce and recruit at the same time usually publish the rule in writing: house leads go to agents on a set rotation, the owner's business comes from the owner's own database, and the owner doesn't sit floor duty.
The number nobody mentions early is what your own time is worth on each side. Say you keep 100% of a $9,000 gross commission on your deal. On an agent's deal at a 70/30 split you keep $2,700. So three agent deals roughly replace one of yours, and every hour you spend recruiting, training and reviewing contracts is an hour off your own pipeline. The first two years of most small brokerages are funded by the owner's personal production, and the transition point comes when supervision starts eating the deals that were paying for it.