Philip Morris was already making noises about not renewing *their* sponsorship contract meaning Desilu would have a #1 show without a main sponsor. Had they signed on, the move would mean the main characters would be seen in interstitial cuts driving to various locations around LA in their new Pontiacs in-show rather than mostly traveling by subway off-camera in NYC.
Lucy's father is never mentioned, and in "Lucy Goes to Scotland", it's said that the McGillicuddy family are her mother's relatives, her mother being of Scottish descent. This would only make sense if McGillicuddy was actually her mother's maiden name.
While her parents not being married wouldn't matter today, the era being what it was would've given Lucy motivation to never mention her childhood circumstances to anyone.