I understand the difference between consistency and bias; one converges as the sample size increases, and the other converges as the number of estimates increases, respectively.
But, I don't understand why people generally prefer the unbiased version of sample variance to estimate population variance. Using simulation, it can be shown that a biased estimator of the population variance can have lower MSE than an unbiased estimator.
So, why do we use the unbiased version of sample variance if the MSE can be higher?
Another question might be how to accurately estimate the MSE without using simulation, since a big component of MSE is Variance of the estimator, and simulation is often not possible since it requires knowing the true value of the parameter/estimand (in this case, the estimand is the poulation variance).