Statistical discrimination is often useful. False stereotypes are problematic, but they are problematic because they are false, not because they are stereotypes. True stereotypes are useful.
“Stereotypes are inherently problematic” nah. If the stereotype is true it acts as a heuristic; priming a person to think along lines of truth False stereotypes are bad, true stereotypes are good; mainly they act as a kind of statistical discrimination, which is often useful along lines of productivity-oriented decision making and so on Stereotypes are by no means “confirmation bias.”
Confirmation bias occurs ex post an observation, stereotypes “prime a person to think,” in your words. That means it would be ex ante an observation. It is what we would call a prior in bayesian logic. A prior is quite other than confirmation bias. All that being said, I do agree with some of your particular criticism of the term ‘mansplaining.’ It has become a weapon of misandric feminists and others who would like to censor communication on the grounds of a red herring.