Aside from saving gas or electricity, why cover the pot? There are some recipes that insist that you have to cover the pot when cooking. For example, in this video recipe for Bolognese sauce (at 7:36).
I understand that this might save gas or electricity by reducing heat loss. But does it serve any other purpose?
I do not consider it to be essential for the food not drying up, since you can leave the pot uncovered and just add a bit more water at the beginning, or add water at the end if you notice that too much has evaporated.
The only thing I can think about is that this might increase the humidity inside the pot, and perhaps the steam will help cook the food or change the flavor somehow. If this is true, what types of food would benefit from cooking with the lid on in terms of flavor?

PS: This is related to Why not cover the pot? but not the same.
It retains heat &amp; steam pressure, so you achieve a simmer or even a boil with less power input &amp; less water loss.
Great for long-cook sauces. Not so good for starchy things which may boil over if you're not careful, or have the pan too full.
As with most things, familiarity with how your stove/pan/lid combination reacts to a slow simmer will determine how well this works for you. If your stove won't drop low enough, you'll burn things, or need to get a simmer ring to reduce the risk. If you tend top make things too wet, you need to adjust over time.
Making anything to an online recipe needs you to be fully aware of how your own kitchen responds to wet/dry/timings. I don't think I ever blindly follow a recipe, I modify to how it needs to turn out based on my own experience with similar ingredients/quantities.
If I guess wrong, then I'm reducing sauce in a flat panic over the last 10 mins… not a good feeling, but familiarity breeds content ;))
There was at one time folk wisdom that said, &quot;if it grows above ground, lid off, if it grows below ground, lid on&quot;… which I have pretty much ignored for most of my adult life.
Sure, potatoes boil best with the lid on, as you obviously retain the heat, but I'm pretty sure I've never boiled a leafy vegetable in 20 years, I steam them… incidentally using the 'spare' steam from my lid-on potatoes.