If jigglypuff were to be owned by Misty, its situation would be more hopeless than it's already proven to be. As an independent pokemon, it is free to appear at any time, but if it were tied to Misty, she would probably take it with her when she went down.
Though it's not like jigglypuff has that much of a chance now. The writers seem to try to introduce new recurring independent pokemon (i. e. spoink), but they don't really work out all that great. The problem with jigglypuff is that it's a one-shot gag. These were better for Johto, where there wasn't that much to be excited about, but in Sinnoh, where things are always exciting (or at least try to be) that kind of thing is no longer wanted. That's why you hardly see the rocket psychics around now.
Which makes me wonder what carnivine is doing around now. Not only a one-shot gag pokemon, but a hash of an older one-shot gag pokemon is extremely out of place here.