The 5.56 was actually made in the late 50s and formally introduced in the early 60s. It would have probably been in development, at least, by the point of the culture freeze.
If anything, the 10mm is unrealistic. The quintessential '10mm' cartridge, the 10mm Auto, was given birth to at the end of the 80s after the '86 Miami Shootout.
However, both cartridges have been present in every single Fallout game.
As for the underused bullets and limited late-game weapons choice, that's kind of one of the issues I have with the game. Weapon upgrades and perks ended up being a placeholder for actual better weapons, so by the start of the late game you've basically seen all of the weapons content and picked the best weapon for yourself. Even Fallout 3 had a few new things to introduce by the late game, like the gatling laser.
Weapon upgrades also reduce the value, essentially, of different classes of weapons. Since, with the right perks, you can readily configure most weapons however you want once you've gotten a single example of that weapon, there's less meaning to finding other versions of that weapon out in the field. At best, you can find Legendary variants, but Legendaries can easily end up being redundant or something you don't want to use, and they make the actual value of finding legitimate 'unique' weapons less important since a generous portion of the unique weapons have the same bonuses you can get from the Legendary system anyway.