Hi!
I currently own 22 budgies, and over the years I've seen so many different personalities. I think many others are right in that sense - some birds are just more shy than others. My two tame babies are very bonded to each other and to me - my female is more clingy, and is constantly on or near me, whereas my male will check in on me throughout the day to preen and groom my hair. I brought them home at 6 weeks and finished the hand-rearing process, so they probably also bonded quite easily to me since I was feeding the directly - however, they are also just inherently affectionate birds, not only to each other but also to me.
About a year ago, I had 5 hand-reared budgies living together. The would sit on my finger and shoulders, but they always chose their flockmates over me despite being super tame. Since there were a few of them, I think they naturally gravitated to their cage-mates over their humans, because it was just in their instincts to do so - however, I also just didn't have the time to spend more than an 1-4 hours with them out of the cage during the day. Now they all live in my aviary with the others, and while they occasionally fly onto my head or shoulders when I go to visit them, they've mostly grown a greater bond with their birdie flock.
As well as this, it is important to keep in mind that if there are one or two wild budgies in a cage of tame budgies, their "wildness" will begin to rub off on their birdie friends. I've also seen this myself - that's why tame budgies should be kept separate if you want them to stay tame.
I can try offer some advice based on these experiences and others that I've had.
1) Spend time with all of your birds as much as you can every day. If you want to be apart of their flock, then you have to truly BE a part of their flock. The more time they spend out of the cage with you, the better. Unless I am going out to university, to run errands or to see friends, my birds are out of their cages.
2) Invest in a bird gym or play stand. This will create a new, stimulating and exciting place for your birds to enjoy when they are not in their cage. This should help to solve their attachment to their cage, because they will have other interesting things to explore in the room.
2) Make sure to spend time near them, but don't pick them up when they don't want to be picked up. My cockatiel was a very shy girl when I brought her home, she didn't like to be interacted with too much despite being hand-reared - but over time of only having her on my finger to take her out of her cage or to help her reach places, she eventually started to coming to me as she trusted me. Now she'll groom me and likes to play a lot.
I hope this helps in some way - it is of course easier to bond with an individual bird than multiple birds, but it can certainly be done if they are all tame and you can spend a good amount of time with them all. If some of your budgies aren't so tame, there are many forums you can find here that cover this. Just recently I answered
this question that might help!
Good luck!


