I think the problem is that most of the crossing accidents are not happening in the most densely populated areas, such as downtown Miami (where the line is already partially elevated) but are happening in low density car-dependent areas, where there is not really the same sort of economic case for elevation, due to the lower density of land utilization and value.
Furthermore, the FEC mainline is not there purely for Brightline, but also carries freight. Putting in elevated sections would lead to the line being much more of a roller coaster, as it goes onto and off viaduct sections as needed. A passenger train with a high power to weight ratio can probably deal with that but it could be crippling for a heavy freight train.