People wax rhapsodic about Mr. Neil--"Old School," "real Mafia," "loyalty above all"...bla bla bla. If he were all those things, he would have given up Quack-Quack and Gotti for all the reasons you said. He didn't. Why? Maybe because, even though he accepted Castellano as Don, he resented him and didn't want to bend over backward to be helpful. Quack-Quack was his nephew, and I guess in this case blood ran thicker than water. Gotti looked up to Neil as a father, and I suppose Neil felt the same.
But in the Mafia, you can never go wrong following the money. Ruggiero and Gotti were dealing drugs, and no doubt they kicked part of their earnings up to their capo. And, maybe--just maybe--those tapes that weren't turned over to Castellano had some talk of Neil's share--meaning that he could have been in mortal danger if the tapes had been turned over.