I The only actual cavern I can think of which is worth diving in FL is Jackson Blue. A cavern card is not really much of a license to learn if there are only a couple sites you can actually dive right?
Peacock cavern ROCKS... Little River is pretty cool too. Ginnie not so much... There is NO excuse for a Cavern student to go past the stop sign EVER... The only standard I think needs to change is 3rds/6ths but that is only based on my opinion not anything factual other than I KNOW people I have dove with violated their guidelines of 6ths...because it just didn't them enough time actually in water... while totally denying that they had pushed their agency standards and were diving 3rds...
Cavern gave me time to get comfortable in an overhead environment... relatively good at frog kick and buoyancy and running a line... still had to do lost line recovery, lost buddy search.... all good prep for moving to Cave1 when I was ready. In fact really feel like Cave1 was a repeat of my cavern course with the exception of actually being IN the cave rather than cavern zone.