Not at all rash Pedro
The US has since WW II maintained a presence in the Caribbean by way of the Second Fleet (Atlantic) and "tasking" or forming a Task force of ships on semi permanent duty in the Caribbean and South America.
There is no credible threat from any Caribbean, Central or South American Countries to the USA or it's allies and certainly nothing that is not easily defended by this task force, and quick response of land based US aircraft that could/would respond to any Fleet threat within hours. (Don't forget those B-1's in Texas which could literally make the trip to almost anywhere in the Caribbean within a couple hours, the BUFFS at Barksdale would be able to respond for sustained mission within hours and the ever present (Or are they) B 2 Spirit Stealth Bombers have a quick trip from Whiteman, all within a time frame measured in hours instead of the "old" way of months upon months of planning
The British ably proved in the 1980's (Falklands or Maldives war) that a smaller well equipped and trained force, with proper intel. could take on numerically superior and better equipped force (Argentinians and their Dassault Mirages, Super Entendars, Submarines) with the aid of mid air refueling and aircraft carriers. The British did not have near the capability of one US CBG yet wreaked havoc on the Argentinians (Seems "normal" for the Brits, under equipped and using cast of equipment they find a way to excel) who many felt would leave the British ships dead in the water with their deadly Exocet missiles (The did have some success but failed to press their advantage of having supersonic Air Superiority fighters versus British "Jump Jets" and instead retreated to protect the Capital of Port Stanley AND preserve thier rAir Fleet as they had little operating RADAR and they were not faring well against highly trained British Naval Pilots.
The US Command is considering or has considered "reactivating" the US Fourth Fleet, a Fleet in name only as it is really a subset of the second Fleet with no permanently assigned assets, which would headquarter at NAS Mayport Florida and be responsible for Narco interdiction, humanitarian assistance a and a general presence in teh Caribbean and South American region
Apparently Chavez, the Argentinians and a few others (Cuba) are not too happy about the reactivation of an entire US Fleet in their swimming hole, but I don't beleive they will assign any carriers to this group, instead staying with fast CG's, DDG's and LPD's to provide helicopter and Marine Harrier support and capabilities
I would "assume" the ever present Attack subs might use the Caribbean now and then, maybe a deterrent to any flotilla of Yolas intent on an amphibious invasion of Homah, Louisiana.
Seriously, today's equipment, both surface and aerial are no longer tethered to fixed station and a Caribbean station is just an unneeded cost
Your second thought was astute
Then again, we (USA) could just build a fence :ninja: