It is a constantly changing bar, but to put some perspective on it, it's not that bad. Having gone through the process, the LFT tests take only minutes. Literally you walk in the tent, sign your name, they swab you and you're out the door. Most hotels do it on-site. For my 3 tests I walked the 5 minutes from my house to the testing site. My tests took 3 minutes from the time I walked in the door to the time I walked out. You don't need to even wait for the results, the assume it's negative and call you if it's otherwise. The worst part IMO is the $90 you spend on them. That's beer money.
This one we agree on. And so does CITA. They are actively working on changing this.
It seems (at present) unlikely that Cayman will shut down again, unless the Sigma variant, or whatever the next wave is ends up having a catastrophic amount of hospitalizations and deaths. There was massive community pushback in October when they delayed the opening.
Just remember though the US requires a negative test to get back in, so I would say Cozumel (or any other destination) has a similar level of risk when it comes to travel complications.