LuanKuci, not really. There was more money for them to join in with a big family such as the Bonanno or Colombo crime family. Especially when it came to interstate unions, or global businesses. Chicago hurt the families west of their city with the yearly tribute they demanded. Keep in mind many of the mobsters knew that life well and did not want their kids to join, plus over the decades there have been better job opportunities for those of Italian descendants in legit business and careers.
When talking about the quality over the quantity, the larger families had a larger pool to pick from and they did have skilled members despite that pool shrinking. The smaller families did not have that pool, hence why it was not uncommon for made members and associates to transfer from New York to a smaller family.