I don't know about Grassy Key specifically but there are a few possible reasons.
One is a contractor started a project but didn't grease the right people. I was fishing in Key Largo once and met a local guy and asked him about the strange canals he had next to his house. He said there is a lot of corruption in the area. Especially with the Ocean Reef Club aholes who have stupid amounts of money. Apparently, years ago, people started canal projects but didn't get their paperwork approved by the right people. The contractors dug out the canals but after their paperwork was rejected, they created a barricade to prevent them from being used. Hence landlocked canals. That's at least what I was told.
Second reason is gov't grabs. I think the gov't came in and bought up property years ago to prevent over-development and environmental damage to the region. It's a fragile environment with unique ecosystems. Also, there are too many people, there is only one road out. The keys are essentially maxed out. The gov't and locals don't want people moving there. At one point, some areas might have been private property but later got turned into NWR land after a hurricane bombed the area out.
Lastly, and I don't think this applies to the canals you posted about, is quarrying. Back in the day, the center of some of the keys were mined out for rock to build the Flagler railroad bridges. If you've ever been to Bahia Honda key, there is a quarry in the back that goes pretty deep. There are giant grouper down there by the way. Another quarry is the horseshoe right after Bahia Honda. The swimming hole on Ramrod Key. There is a large one located in the Key Deer Wildlife Refuge on No Name key.