A good "reason" for parodies is the cathartic experience of doing in a song you've been requested way too many times: verbal revenge!
Quickly coming to mind:
The Boxer becomes The Folkie "I'm a lead fingered folkie..."
Waltzing with Bears becomes Golfing with Hares
The Garden Song begets The Anti-Gardening Song "Slug by Slug, Weed by weed"
Barrett's Privateers becomes Mickey's Mouskateers

Admittedly, a badly written parody is a particular type of dreadful, but there's plenty who write witty parodies. Les Barker stands head and shoulders (when he's on a soapbox) above in that category. His My Husband's got no Porrige in Him parody of My Husband's got no Courage in Him is something I can sing to audience who have no knowledge of the original, & don't care that it's a parody - that does not detract from their enjoyment of the Barkeresque peculiar plotline.

In some cases, there's a thin-to-nonexistant line between parodies and just using the tune of another song for your own lyrics. There's a whole genre of music called"filk" songs that relies heavily on parody, bending the themes of Science fiction subjects (also popular with the Society for Creative Anachronism). A good deal of this is on the drek end of the spectrum, but... there are moments....
Simply re-using a popular tune for a new set of lyrics is a very common way of making up songs for specific occasions like anniversaries, retirements, political events or birthdays. I was serenaded to "Oh Joannie O Joannie..." to the tune of Clementine on the occasion of my 50th birthday. It was totally embarrassing, immensely gratifying and possible for everyone there to sing.

I think the mostly humorous nature of parodies is what I enjoy the most. Perhaps you've just not heard a parody that tickles your particular sense of the absurd?

Joanne in Cleveland