This is my speculation.
It probably was not common for children to write their fathers during World War I because most of the men were young and didn't have children. The big preference was for young unmarried men, as young as eighteen. Furthermore, the U.S. involvement in World War I was not as massive as that of World War II. They were probably not drafting married men during World War I at all. During the Second World War the government was not drafting married men at first, and especially not married men with children. A lot of men were getting married just to avoid being drafted. Later, however, as the war became more extensive, and there were heavy losses through casualties, the government began drafting more and more men. Even so, most of them would not have children who were very old
In our present era it is very common for men and even women in the armed forces who have spouses and children at home. But it wasn't like that during World War I. Nowadays, servicemen and women volunteer for careers in the military, so it would be natural for them to marry and have children.
I believe the mail service between the U.S. and Europe was fairly good, if slow, during World War I, and the servicemen were getting a lot of letters from sweethearts, wives, and parents.