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I get the feeling it was originally conceived because the devs wanted to have something in place for players who made the connection between "it hatched from an Egg" and "it can probably lay more Eggs."
Phione was the perfect compromise: it avoided devaluing Manaphy (because you can't get more Manaphy - Phione is instead), but it also avoided disappointing those players (because you do get SOMETHING for breeding Manaphy) and it had value on its own for being a cool secret that even people who had Manaphy might not necessarily know about unless they also thought creatively and didn't just dismiss the idea over the notion that Mythical Pokémon can't breed as a "rule."
As for whether people like it... I can't speak for everyone, but for one thing, I think its design is better - I think its defined body style is cuter than Manaphy's blobbish one, and its color scheme is more appealing to me - and I also like it for nostalgic reasons, because my brother surprised me with a Phione when we were kids and I just thought it was the coolest thing.
The "story" behind that gift is basically that he had mentioned wanting to give me a Pokémon as a present, but when he asked what I would want, my response basically amounted to "I would be happy with anything" - and my reason was approximately that "obviously Legendary Pokémon are really cool, but even just a Pokémon I don't have would be awesome, because then I can breed it and get more and it's probably easier on you since you can also get more than one!" So of course he decided to get me the one Pokémon that was BOTH Mythical (considered Legendary at the time) AND possible to breed, and one of the only Pokémon you couldn't get at all in DP.
I know most people think of it as a "consolation prize" or a ripoff Manaphy, but just because of that anecdote and knowing that I thought it was the absolute coolest thing as a kid, it's just nostalgic and I appreciate it that much more now. I don't think it's as pointless as people say!