My current operating theory is that stardates are an invention of Starfleet Command and provided for in the Articles of the Federation. The purpose of stardates is to provide a means of the entire fleet, and eventually basically all civilian traffic, to coordinate actions throughout the galaxy.
The first mention of "Stardate" in-universe was in the Enterprise episode "Damage". I quite like the idea that the Federation adopted the timekeeping system of their former enemy, the Xindi.
As for the Abramsverse dates, yes it's Earth-centric, but it's nice to have such an instantly-understandable system after the random digits of TOS/TAS and the convoluted mess degenerating into random digits in TNG/DS9/VOY.