LP--
You are making the irrational assumption that state and private actors always make rational decisions.
Why did Puerto Rican nationals try to assassinate then-President Truman in 1950? Surely, if successful, such an assassination would have only backfired.
Remember, when ideology and nationalism, or ethnocentrism, or ethnic bias get involved, rational thought and behavior often goes out the window.
The Alpha-66 crowd said that they had been betrayed by JFK, at BoP, and their friends and comrades died for nothing.
The G2-DGI'ers knew that JFK had been trying to assassinate Castro for years.
A couple-three hotheads....a couple guns...all you need.
As for LHO being "nutty"...that might be viewed as a plus. A nutty LHO's testimony might be taken with a grain of salt, and more-easily dismissed, providing plausible deniability.
Anyway, I am not sure LHO was regarded as all that nutty pre-JFKA.