i think the problem is there are no fundamental changes after some is like 20-25 years old, the bones mature, the brain mature etc, then comes the accumulation of trash what we call "becoming older"
That's just when it starts becoming noticeable. The damage begins to accrue in the womb. Small children show evidence of UV damage to skin, for example, and the beginnings of atherosclerosis can be seen in some teenagers. Most telomere loss occurs in the early years of life. Aging does accelerate late in life when certain forms of damage lead to higher rates of accumulation of other forms of damage, in an ever-increasing spiral.
Do You think, that they will find it interesting to find the genes, responsible for this "not growing" disease?
Yes, I think that it will eventually be understood when development is fully understood. Someone should get a DNA sample from these people and sequence it. It might provide some insight into normal development, and might even lead to a work-around that would allow them to continue developing.