Your framing is close and the arithmetic holds, but the 30 percent retained share is doing more work than the overhead figure. Retained share is not the split on the sign. It's the split net of everything you give back: sign-on concessions, capped plans where a producer stops paying you after 15k or 20k a year, referral fees on company-generated leads, mentor splits paid out to whoever trains the new agent. A firm advertising 70/30 often retains 18 to 22 percent blended. At 20 percent your 2,700 becomes 1,800 and your break-even goes from 54 sides to 80.
Also check the shape of your roster, not just its size. In most firms the top fifth of agents produce well over half the sides. So 14 agents at four deals each is a spreadsheet roster. A real one is three people doing ten, four doing three, and seven doing under one, and the seven consume the most supervision time per dollar of revenue.
So yes, recruiting is the engine. The reason experienced owners don't say it that way is that recruiting without retention is a treadmill. If your annual attrition is 25 percent you're replacing four heads a year before you grow at all, and each replacement costs onboarding, MLS setup, and your own hours.
The risk you haven't raised is your own liability. Every agent you add is a file you're responsible for reviewing, and post-settlement that means buyer agreements and compensation disclosures on every deal. Fifty agents you cannot actually supervise is a worse position than twenty you can, and E&O premiums and deductibles reflect claims history. Growth that outruns your file review capacity is the way this model breaks.