Reasons: I don't always have my laptop on me, and I would like to be able to check up on my pets! Sometimes I go days without being anywhere near a computer, and I really worry about them being fed. I'd rather not give someone my password to have them babysat, and what if I was gone so long the food in my food pen ran dry? Of course I usually get on every day, but I do have to travel (for work and such) and it would be awesome to have my pets in my pocket. Also, it could help with business. Maybe you could have certain items you could only buy in the cash shop on your app? Or maybe even you could make buying the app itself have a small fee. And don't forget about the people who are nosy shoulder peekers, who will then ask "What's that, it looks pretty neat!" Thus making your member base grow.

In conclusion, I honestly think it would make things really convenient, while also helping support the site. I hope you consider this as an idea!