Likewise, no one seems to be advocating all intersections be converted to non-ground-level intersections
Most of coastal Florida has an elevation of less than 5 meters above sea level — just over 16 feet. While other regions may or may not have grade separated right-of-way (Mid-Atlantic, for example), it would be cost-prohibitive to construct RR underpasses for all or most of those existing level crossings without elevating the existing rail lines to boot.
Closing even some of those crossings could and probably would only add to surface roadway congestion, just as what urban expressways have done since the mid-20th century. Sloping new underpasses at those crossings not only requires provisions for pump-extraction of storm water (as done in Norfolk, Va. at Hampton, Tidewater, and Va. Beach boulevards), but it also would require condemning or partial truncation of many existing properties adjacent to the crossings, in order to safely accommodate the lowering of roadways. Lowering the railroad right-of-way itself — similar to what Reno, NV did — would be too risky for the railroad in such a region.
Perhaps the most topographically feasible alternative would be to build an elevated right-of-way alongside the existing one, but that too would require land acquisition against far too much pushback. It might be feasible to elevate a new rail support structure above the existing tracks without being too disruptive and destructive. That too would be very costly, but that option also might be one of the few possibly tenable ones.
Unlike with segments of the new extension to Orlando, level crossings on the existing runs were inherited from a distant (erstwhile) period. That said, grade separation is the only form of ensuring interference-free operation of higher-speed trains, especially in such a densely intersected region.