And it's usually discouraged by regulators because it can lead to p-hacking. I.e., with a good enough choice of control I can get anything down to 5%
The fundamental problem is the lack of embrace of causal inference techniques - i.e., the choice of covariates/confounders is on itself a scientific problem that needs to be handled with love
It is also not easy if you have many potential covariates! Because statistically, you want a complete (explaining all effects) but parsimonious (using as few predictors as possible) model. Yet you by definition don‘t know the true underlying causal structure. So one needs to guess which covariates are useful. There are also no statistical tools that can, given your data, explain whether the model sufficiently explains the causal phenomenon, because statistics cannot tell you about potentially missing confounders.
Yes, but this is not usually done.