What is the purpose of simmering uncovered?
It thickens the liquid – According to Roy F. Guste, Jr., author of The Bean Book, the proper way to thicken the liquid is to mash some of the beans against the inside of the pot, stirring those in, until you have reached the texture you want in the liquid. This makes the liquid a sauce or gravy of the beans themselves and allows a better coating over rice or other foods. Or you can simmer the beans longer, uncovered.