Gotti's flamboyant style was one of the many things he did that led to the demise of the Gambinos. There are more factors to look at than Gotti loving the cameras.

One example given by Pizzaboy, his no plea policy.
The fact that his capos had to report to him weekly, which was used as evidence by the feds.
Killing Castellano caused a rift I believe in his family. I think it was daniel marino a gambino capo was in the plot to blow him up.

These are a couple of examples, but the reason I think people bring up the media and flamboyant thing is the fact this all contradicted the whole idea of a secret society/the mob.