No, I've had two parakeets now and I personally didn't want them to be fully flighted because I was too afraid that they would get hurt or lost.
My last parakeet, Buddy, was very tame and friendly. I had his wings clipped when I first bought him. He was really easy to tame. I took him out of his cage all the time to hold him and pet him, and I would take him to the bathroom to play and get exercise. He would take short hopping flights, and he loved to chase a plastic toy ball.
My newest parakeet, Chipper is also really tame and gentle, and likes to be held, even though I've only had him for about 2 weeks. I had his wings clipped too.
To me, I would think that it's much easier to tame and bond with a bird if you have its wings clipped. Otherwise, it's just going to take off and fly away from you as soon as it gets the chance, and it'll never learn to trust you. Buddy got VERY close to me, because he learned to trust me and then liked being with me.
Personally, I say you should have Little Blue's wings clipped IF you want to tame her. It might be harder to tame her because she's living with other parakeets and so she's already close with them and might not want to bond with you. But it might be downright impossible to tame her if she's fully flighted, because as soon as you try to pick her up or anything, she's just going to take off and fly away.
Both Buddy and Chipper were very easy to tame, and from what I've been told, most parakeets are. But my situation is different because I only ever had one. I read that it's easier to get a bird to bond with you if it's kept alone and you give it a lot of attention.
I can't have Chipper fully flighted, or any other bird I get because my house is cluttered and there are just too many places where he could get lost or get hurt.
A wing clip is completely painless for the bird (it's like getting a haircut), and to me it just seems a lot safer for them. Just be sure you go to a place where the people know what they're doing, like a vet or a REPUTABLE pet shop with experience with birds. I got my birds from a bird farm, and they take great care of their birds. If a wing clip is done right, the bird should still be able to fly a little bit, so that it can safely glide to the floor in case it falls. And they can fly across a room, but they just can't get that high and can't fly that far.