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.