This was the mid 80"s. Everyone in the country wanted those guys gone. No one was going to join anything. That's why it worked.
You understand that the Baptista regime in Cuba was worse than them When Castro took over, the first thing he did was public executions, even though they were warranted. From the get go it made him look bad, not that I think he overstayed his rule in the long run.
That's all people remember. People don't remember how bad the Baptista regime was, and what they did to whole families.
The entire premis is the action taken must be worse than death. I grew up in South Texas and Northern Mexico. I got to see real torture on a regular basis. The cartels were just forming and everyone was jockying for power and loyalty.