statistics

You need to distinguish between the mathematical-theoretical field of statistics, which is a branch of mathematics just like any other branch of it, and its application in the world. The application in the world assumes different assumptions, and they are of course not necessary. Just as applications of other branches of mathematics are not necessary, because the application always assumes assumptions about the world. See column 50 and more on this.
For example, statistics (actually probability) says that the chance of a certain outcome on a die is 1/6. There is an assumption here that the die is fair, and that is not certain. Beyond that, it is clear that a certain roll will give a random result that statistics cannot predict. If you roll a lot of rolls, there is the law of large numbers that the distribution will approach the theoretical probabilities (1/6 for each face), but even this may not happen in practice because that is the meaning of statistical prediction. And yet the statement that the probability is 1/6 is mathematical and necessary. The problems are only in applications and uses.