No, but the PGA does. I know this isn't a PGA event but clearly they don't want to see ratings for arguably the golf world's favorite tournament of the year down 30% YoY.
Golf has the same problem that baseball does in that there is no shortage of young, marketable talent but it is simply not well-known by people who don't actively follow the sport. Baseball's struggles perhaps make more sense in that historically it has been more of a team-driven league than a individual/player-driven one (in contrast to the NBA and NFL), but golf is an individual sport.
If having Rory, Spieth, Jason Day, DJ, Rickie Fowler, or someone else go on a Tiger-like run of winning majors is what it takes to create a face of the sport, then golf is going to be waiting a very long time. There will never be another Tiger.