Why should rice be cooked uncovered?

There are a lot of different methods for cooking rice. If you use a method that is intended for uncovered cooking and cover the rice, the rice will turn out waterlogged.

If you want to cook your rice covered, you have to follow a method that is intended for covered cooking.

You can cook rice covered or uncovered, it will not impact the flavor. The amount of liquid you begin with, and your cooking time, could certainly be impacted. There are several methods for cooking rice (covered, uncovered, and both). If you are using pre- or par-cooked rice, the directions are likely just a finishing step, formulated so that you don't over-cook the product. You could still use a cover, but would likely need to keep a close eye on it or experiment a bit to get a result you like.

Apart from the other answers given, certain types of rice and lentils when being boiled, create a lot of froth and bubbles. When the vessel is closed, these bubbles do not break up easily, and they build up and spill over the vessel. They also sputter quite a lot and leave a mess over the stove top.

If the recipe did not require you to wash the rice, then it would explain a lot. Without washing the rice, you'll be getting a lot of excess starch in the grains, and boiling with a lid on would likely result in it foaming-over (usually making a mess).

Did the recipe specify to cover it after the water is absorbed, or not cover it al all? Typical instructions for cooking rice on the stove include covering the rice after it boils.