"why does the penis stop growing DURING puberty?"
Because if it didn’t it would get too big to do it’s job.
Androgen Receptor in the Human Foreskin
Changes in amount and intracellular distribution of androgen receptor in human foreskin as a function of age.To provide insight into the factors that control growth of the penis we measured the amount and intracellular distribution of specific high affinity androgen receptor in foreskins obtained at circumcision from 49 males varying in age from newborn to 59 yr.
Total (cytosolic plus nuclear extract) androgen receptor decreased from approximately 40 fmol/g tissue weight in newborn foreskins to approximately 25 fmol/g by 1 yr of age. The amount of receptor rose in childhood to approximately 180 fmol/g in the late teenage years and fell thereafter to approximately 20-40 fmol/g in men older than 40 yr.
The amount of receptor in the nuclear fraction increased at the time of puberty and subsequently decreased in parallel with the decline in total receptor level. These changes in androgen-receptor amount are similar when expressed per milligram DNA or per milligram protein.
I only present this for discussion, I’m not qualified to speak on this subject since I am almost completely ignorant in the chemical and biological fields.