One of the principles that comes out in discussions about drinking and doing mitzvot, is that the alcohol impairs one's self control, and thus they aren't doing the mitzva properly [e.g. some sources here].
This presents what seems to be a paradox, because if one loses self control, one cannot be commanded. This is a fundamental principle of Torah and one of the 13 principles of faith, and discussed in our hashkafic works extensively; that a being that is not capable of self control, is not commandable.
Therefore the commandment to not do certain mitzvot while drunk seems to imply that we are never allowed to get drunk, because then we will be in a state where we are uncommandable, and there are commandments that apply to that state!
How to resolve?