It helps to be located in such a huge geographic area that produces so much great talent.
Also, don't forget, the University of Florida was very scared of the geographic might of SoFla back in the 1950s-1970s, they resisted legislative efforts to put a state university in that area. At one point, UM was even considering affiliating with the state as a "State university" and we were blocked by UF.
FIU boosters will try to tell you that UM similarly tried to block them from becoming a state school, but it was more the UF guys. There were a few UM guys who were perturbed about UF blocking us, and then the state doing an end-run and building a "new" state school in Miami, but those Gators really know how to protect their turf. That's why FIU had to be "International" and FAU had to be "Atlantic" instead of, say, UF-Miami or UF-Palm Beach.
Now we just need to get an indoor practice facility (lots of lightning storms in SoFla, and it is apparently now on the Athletic Department's radar) and an on-campus stadium (still, for the most part, a dream, though we are secretly preparing for it with parking garages).
I wonder if that explains how USF and UCF got incorporated at that time while FIU and FAU came into existence later.
UCF was (unfortunately isn't this year) was a laughing stock for decades in football, and they had no legendary coaches to bail them out.