Ive been there plenty, its not like SF Bay, but its very shallow and in fact you have to be careful not to run aground even if you are out of sight of land. It is a bay because it is between the Florida Keys, and the Florida Coast. The Keys are not just a chain of islands, but also a very shallow bank that separates the Gulf of Mexico from the Atlantic Ocean. The Florida Bay, is a Bay that is part of the Gulf of Mexico.
So not only is it not an Ocean, it is a bay that is part of the Gulf, two times separated from the Ocean.
It is managed and policed by the Federal Government. If they allow people inside while enforcement of the regulations that keep it a healthy ecosystem is not available, the area would be plundered by fisherman, boats that would harm delicate reefs, and the waterways that are maintained by the federal government will become more dangerous. As to if policing to keep it "closed" is more expensive than allowing it to remain open, I seriously doubt that claim. Id like to see the numbers. The fact is however that it does not matter, the Fed's are currently allowed to spend money on essential personnel, like to keep people out of a closed area, but not allowed to maintain a federal recreation area. That's the law like it or not.
Additionally, suggesting that these are decisions the White House is making is just pure disingenuous crap!
If Obama had an (R) next to his name, you would not be hearing about this, from the likes of Glenn Beck and such.