the idea is mourning. you tend to fixate on the chest beating as if that was the object of azadari.
as for all Prophet being humans, that is true, but that does not dilute for one minute the fact that everytthing the Prophet did in his life was worth following. Thereby, feeling, expressing grief for those fallen before you is sunna.
if mourning is “forbidden” , not even the three days you graciously grant, then did the Prophet sin when he did mourn?
Didnt the prophet request people in medina to mourn for Hazrat Hamza?
As Mahomet and his followers reached the foot of the intervening ridge, the whole company at his command, fell into two lines, with the women ranged behind, and there they offered up prayer and thanksgiving to God 68. Drawing near to Medina, they passed the habitations of the Bani Al Ashal, whose females wailed loudly for their dead ; - “And Hamza!” - cried Mahomet, - “Alas, who is there to weep for him!” The wounded men here received permission
to go to their homes 69. The rest followed Mahomet to the great Mosque, which they readied in time for the sunset prayer 70. It was a night of mourning at Medina. A sense of insecurity still pervaded the city; the chief men again kept watch over the Prophet’s door, for fear of a night attack from the Coreish 71. Some of the wounded remained near the Mosque, and the fires kindled for them cast a fitful and lurid light around its courts. Mahomet slept heavily, and did not answer the call of Bilal for the second evening prayer. Shortly after he awoke, and walking forth, asked who it was that wailed so loudly near the Mosque. It was the women of Medina, who had heard his pathetic words regarding Hamza, and came to mourn for him. Mahoinet blessed them, and sent them to their homes. Ever after, it was the custom at Medina for the women, when they mourned for their dead, first to wail for Hamza 72.