Randomisation and balance in experiments
Ok, I am far from an econometrician, but my train of thought would be as follows:

By using random assignment we have two groups that are on average equal to one another on all aspects. As you rightly point out due to sampling variation there will be differences.

My worry would be that if I start "correcting" those after randomization (as per your example with gender distribution) I introduce other differences between the groups in say age or even an unobserved but important characteristic.

Stratification is different as it is done upfront. You have a characteristic that you know is different for different groups so you take the random samples within those groups. As a rather naive example: we know that the effect of taking anticonception pills is rather different for men and women, so if you wanted to test the effect of the pill on fertility you could stratify by sex and then do a random assignment within the sexes.