It really just depends on the bird. I had a female handfed budgie who absolutely loved having her head and cheeks scratched when she was little, and grew up to hate being touched.
Before her, I had a parent raised male (Pippin) who didn't learn to enjoy being petted until he was four or five years old. Before that, he would act somewhat scared and confused if I tried - I think because he saw fingers only as perches. One day, I caught him rubbing his cheek on a perch with his eyes closed and took the chance to scratch his head for him. As soon as he realized what I was doing, he decided that it was pretty good, and loved to have his little head scratched. I could tell how he was feeling by how much he wanted his head scratched. If he was feeling well, he would want me to scratch his head for a minute or two, and would then fly off to play. When he was molting or had had a scary experience, like a vet visit, he would want me to scratch his head for a much longer time. When he was feeling sick, he just wanted to be held and his head scratched as much as possible. He would fluff his little head up to let me get in there to scratch and would butt his head into my finger to ask for more scratches if I stopped. So he got more cuddly with age.
The budgie I have now, Sammy is a handfed male, but has never wanted scratches, not now or as a baby. Like Pippin, he seems to think of fingers only as perches, and becomes confused and upset if I attempt to scratch his head. I hope to someday get him to let me scratch his head.
In any case, my experience with Pippin would suggest that they don't become less cuddly with age at all - he in fact became more cuddly with age as he seemed to find it very comforting when he didn't feel well.
Oh and of course by cuddling, I mean only cheek/head/neck scratches, never any petting or touching on the body. That's something almost all budgies dislike, it's just not their nature. You almost never see wild budgies snuggled up together like you do with wild cockatoos, conures, ect.