This is basically a question of thermodynamics -- you have a system in which there is heat being applied from the bottom, while being cooled from the top.
If there's a lid on the system, then you retain moisture in the space above the sauce, which reduces the amount of evaporative cooling. This means that you need apply less heat to the system, and it results in less of a temperature gradient through the sauce.
It's this temperature gradient that gets you into trouble -- a thick tomato sauce doesn't convect the way that a thin stock might, and so you'll get scorching (burning) on the bottom of the pot ... which can ruin your sauce.
As such, it's much more maintenance to cook the sauce with the lid off -- you have to stir it much more frequently. You can also end up with a slightly more "roasted" flavor to the sauce, as the higher heat at the bottom of the pot can caramelize the tomatoes depending on how often you're stirring it.
And there are things lost besides moisture and energy.
Volatile oils will be released into the air above the sauce, and if you have the lid off, they will go into the kitchen. This might make the kitchen smell great, but it can reduce the flavors in the dish being prepared. (although for some things, like cabbages, you intentionally cook lid-off so that the sulfur compounds don't stay in the dish)
And there's the cleanliness issue. Tomato sauce is notorious for spattering as it simmers. If you have a very tall pot that's not filled to the brim, this might not be an issue, but if your sauce level is near the top of the pot, and you've got the sauce at a simmer, the bubbles will burst spreading droplets of sauce all over your stove.