I enter this topic late, but I'd say there are several reasons Gotti was liked and popular.

He was a career gangster who truly lived the life, which garners respect.
He was a flash dresser as he got older, not a dirty street scumbag thief.
He had family power and a long, strong association with Neil Dellacroce.
He was successful as a gangster. Drugs, sure, but who moralizes in LCN?
He was a high flyer who didn't fly beneath the radar - he WANTED attention.
He was unforgettable: he had fans & wasn't interested in staying in the shadows.