To add to that, birthdays can clump, just like any seemingly "random" data.
A million dots scattered randomly over a graph can all land on the exact same coordinate if it’s truly random.
What most people intuit as random is some sort of noise function that is generally dispersed and doesn’t trigger the pattern matching part of their brain
Not significantly. For actual births, a couple holidays have very low rates but clumping into much higher rates happens on no dates.