As we know, if we are doing many tests or multiple comparison, we don't use the same $\alpha$ value and use some $\alpha$ correction methods like Bonferroni. This is done because when we do multiple tests, we have higher chance of getting something as significant compared to doing for fewer numbers of tests.
But my main question is this:
1) It is said if you are comparing multiple sample means using ANOVA and once you find there is some significant difference then you can do a post hoc analysis by doing pairwise comparison. But now you don't have to actually do a Bonferroni correction. Why is that? Isn't this post hoc analysis same as other pairwise t test where we use Bonferroni correction?
2) If Bonferroni correction is required because more tests leads to more chances of getting something significant then why we don't use the same thing, where we are doing something like regression where we are testing significance of $\beta$ estimates, or whether a variable is significant or not for feature selection using p value/F score? In that case also we are doing multiple comparison in checking whether each variable is significant or not. Then why don't we use Bonferroni correction on critical $\alpha$ there?