ambiguity doesn't necessarily increase the appeal, it can just increase the blandness, compared with putting some specific details in.
However, yes, with a little bit of thought (not necessarily a lot) ambiguity can really help the appeal. I used to know one songwriter who always wrote her lyrics in a way that could be interpreted as some sort of love song, even when the song might "really" be about death, or friendship, or conservation, or the rain, or religion. She felt that her songs should always have at least two possible levels of meaning in that sense. It works well in my view, though i think as you say it depends on each song, sometimes they are little vignettes just about one thing and whatever emotions are connected to that one thing.
re: censorship, well, writing is censorship. You basically cut out everything until you are down to the exact song, finished into the way you want it to be. It's not really "censorship" in the normally understood sense though, but it does bear remembering (eg: i don't like rhymes that i find trite (moon/june/spoon etc) so i would "censor" them out of my writing, if i found myself doing them inadvertently (by writing something better for those lines).
But in the sense we're discussing (ie: not putting people's names in, not saying really really how we feel or think, and so on) then no, i no longer do that. Like most people (i imagine!) i started off writing with a conscious view of how people would put themselves into the songs, parents, friends, etc. I was careful not to refer to them in a song unless it was specific (a love song to my girlfriend when i was 17 deliberately included her name for example, and when my dad died, i wrote a song with his name as the title).
But then people would still ask me if such and such song was about them, or about someone else (usually they'd only be interested when they thought it was about them, though!), and it never was! So i just thought well, i can just say what i like then, and so i did.
It was really making me nervous actually, not being able to say what i felt in my songs, and not being able to be adventurous either! For me it was mainly things like, i want to write a song with a murder in it, or maybe a song about two timing somebody or any of a million other things that wouldn't actually be happening to me literally at the time. Once i realised it was okay to write about all that stuff it was very liberating.
Nobody really listens to my songs nowadays, and i don't play live any more so it's academic now. My songs go on the internet and people can take them as they find them, i know by now that other people write whatever they like, so why not me? I wish i'd learned that lesson earlier, for sure.
