In Murder Machine there's this anecdote where Nino Gaggi tries explaining to Roy DeMeo that he wouldn't like being made.

Even tho the real reason was likely cause Castellano was against it, Gaggi said that Roy had more freedom as an associate. He didn't have to adhere strictly to the rules and be held as accountable as a made man does.

So perhaps that's another reason connected guys turn down their button, especially in a day where the other pros of being made can be undesirable