Generally only good songs give rise to good parodies, and they in no way diminish a or damage the original song.
All right, you can have a parody which is destructive, maybe of some song that the parodist thinks is a terrible or wrong-headed song. But most parodies are more in the way of tributes.
The best parodies I've ever come across were the Kippers -the great thing there was that they weren't that close, but just close enough, and they would turn the tune around as well as the words. And yet you recognised it, and it would build on some potential absurdity in the original which had never occurred to you. Most parodies are trivial, but not these ones.
And I'd distinguish completely between a parody, and a song that uses an existing tune, or an existing song structure, and yet is a new song. Some of Ewan MacColl's best songs did that, and I'd never class them as parodies.