I just see them as a way to discriminate. I get that if an alien invader comes and attacks Earth, it would be ideal if all countries and all races just band together to fight them off, but it is more ideal if they all joined under one flag.
Anyways, now I just feel like recruiting only women from English-speaking country/flags. English because the voices would make sense since they all speak with English "accents". Women because that's a personal preference.
It is a pain though to waste so much money recruiting, then dismissing the majority of them.
My team is always all women. It adds some spice to the otherwise generic soldiers (since they're all stat clones). Could have used more specialization, though -- their hairstyles all look similar, and one of the women's hairs has a graphical bug that causes it to explode.
As for flags, read the "tips" that appear when you load the game. One of the tips is "pay attention to the country which provides experienced soldiers". I have a feeling that some countries are more likely to give soldier rewards (for successful terror missions) than others. I never paid attention, though, because I go for engineer rewards than soldier rewards. Besides, I have an all women team, and soldier rewards are random.
If it really bothers you, there's a mod that changes all flags to the X-com logo.