Now that's the real difference between a native and a non-native speaker: As a non-native speaker, I'd probably put about the right amount of articles in there, but I can't even imagine why dropping them sounds 'cutesy'. Probably most of my sentences randomly project 'cutesy' or 'geeky' or 'obnoxious'. And it happens on a subconscious level even if you know that I'm not a native speaker.
Referring to "a baby" as "baby" is cutesy because it kind of treats "baby" as a name, or perhaps because it immitates the way young children talk. In normal circumstances dropping articles just makes you sound foreign.
