Why would an appellate lawyer market to other lawyers instead of just the public?

Because a real share of appellate work comes from other lawyers, not directly from the public. Trial lawyers bring in appellate counsel as specialized outside counsel, sometimes after a loss, sometimes before judgment as embedded appellate counsel, and sometimes to defend a win on appeal. That means an appellate practice's marketing has two real audiences: people who need an appeal handled, and lawyers deciding whether they need appellate capability on a case they're already running. Attorney-to-attorney marketing and referral relationships (including channels like the Florida Bar's own Attorneys' Exchange) speak to that second audience directly.