The "funny" part is that restrictions on bullet technology date back to the 19th century, 1868 if I'm correct
The first treaty specifically naming expanding ammunition was the 1899 Hague Convention Declaration III On The Use of Bullets That Expand or Flatten Easily (the 1899 treaty). According to the terms of this treaty, “The Contracting Parties agree to abstain from the use of bullets which expand or flatten easily in the human body, such as bullets with a hard envelope which does not entirely cover the core or is pierced with incisions.” Long story short this treaty does nothing to prevent the US from using expanding ammo. The US is not a party to this treaty. The treaty does not even apply to all types of conflicts either.
There is a second treaty, that is much more recent addressing expressly expanding ammunition. The second treaty is the Rome Statute of the International Criminal Court, 17 July 1998 (ICC statute). This treaty makes use of expanding ammunition in certain types of conflicts a war crime, but has not applicability to others.
A lot of other treaties and international law depends on whether one says that expanding bullets cause unecessary suffering or superfulous harm.
What is really interesting is that the same arguments about guys not going down have been made from the time the British first moved to FMJ bullets in their campaigns in Africa. These arguments and public comments are strikingly similar to much of what is said today about 5.56. In 1903 in fact, when 200 British soldiers were overrun in Somaliland, part of the blame was placed on the ineffectiveness of the Mark II (a FMJ 303 cartridge that replaced the British Dum Dum) and an updated Dum Dum was issued again and then later again replaced by another FMJ cartridge.