Every single nation on Earth has mandatory paid vacation, except for the United States and three tiny islands: https://en.wikipedia.org/wiki/List_of_minimum_annual_leave_b....
Edit: And looking into it a little, I'm pretty sure two of those islands actually do have mandatory paid leave after a minimum period of employment.
Mandatory vacation, like education, mandatory IDs, and myriad other laws are the sole jurisdiction of the individual States to decide. There will never be a "US" law about these things. Most questions that start with "why is the US the only country..." can be explained by the fact that the States decide and the US government can't force the States to make laws.
Similarly, there is no US law against most crimes. It doesn't mean those laws don't exist in every State.
That said, there is no State with mandatory paid vacation either AFAIK.
Given the political diversity of the States, this suggests that mandatory paid vacation is either not considered an important issue by people across the political spectrum or there are existing regulations that would create real problems if there paid vacation was mandated without changing those regulations first.
It would be interesting to know which percentage of full-time jobs in the USA get no paid vacation.
I don't get what the big deal is about mandatory paid vacation. My view is that your total compensation will be set based on the market value of your labor. Some portion of that compensation is given to you in the form of ordinary wages and some portion in the form of paid vacations. If the government mandated paid vacations would it increase many people's total compensation?