Heat conducts though the bottom skin of the lid from the mash into the airspace of the lid. Once there, it moves around through convection until it hits the top skin of the lid. Then conduction happens and it's lost to the ambient air. Foam and other insulation stops conduction by creating countless isolated air spaces. If open air spaces were better, like augiedoggy said, no one would waste money on insulation but would just caulk everything and call it a day.
The 2 major heat transfer phenomena that are relevant here are Conduction and Convection. Conduction is the transfer of heat from one object adjacent to another. The rate of heat flow through materials is expressed as thermal conductivity values. Thermal conductivity expresses how easily heat can transfer. Stainless steel has a value around 16, plastic around 0.2, and air 0.02. So heat transfers much better through steel than through plastic, and least conductive is air. If you're unsure of this go ahead and do the Google research.
The other phenomena of Convection is the transfer of heat to an adjacent moving field- like liquid through your wort chiller or in this case the air next to your wort. There is Forced Convection which is air/liquid being pushed past an object by force like a fan or a liquid pump. And there is Free Convection which is the effect of gravity coming into play as air gets less dense and wants to move higher. This movement of air provides an amount of convective heat transfer.
Applying these principles to your cooler, with the small volume of air trapped in your lid, and the fact that it is sealed (no holes to outside air), you aren't going to have much/any Free Convection going on. So filling it with foam is pointless. As previous poster pointed out, the value of foam/fiberglass is the fact that it creates air pockets between 2 layers. The reason that is beneficial is because air conducts heat very poorly. But it also helps where you have convection because it has physical structure to it that can stop air movement. In your attic and walls of your house where you have large volumes of air and a non-sealed condition, insulation is necessary to stop the convection. But for your lid, it's pointless.
For the airspace above your mash in the cooler, although Conduction through the air is poor, you've got Free Convection to consider. The more air space, the more potential for the phenomena of heating the air closest to the liquid, this air moving towards the top, and colder air replacing it moving down. If this movement of air has the ability to go out the top and swap its warm self out for colder air outside the cooler, you also have that to worry about. For a cooler to work as a liquid dispensing system, it naturally needs to have a way for air to come in through the lid as you pour liquid out the bottom. So it will by design not be air-tight. You could duct tape around the crack, or find the designed-in air leak path and stop that (such as a groove molded into the underside of the lid). Putting something in this air space to physically stop the air movement as hot air tries to move above cold air would also negate this Free Convection. So filling the space with a foam block, Ziploc bags filled with air, sheet(s) of aluminum foil, etc. would also help.
For all the "What about this?" thoughts pending out there, I'll apply this logic to some other objects.
Why isn't the walls of the cooler filled with air instead of foam? Because air is not structural and to mold the external walls and internal walls separately and ensure they maintain a good gap all the way around is difficult. It's easier to fill it with a structural foam to keep the gap between inner layer and outer layer.
How do double-wall vacuum insulated drink containers work so well? Because they are small volumes of air trapped in an air-tight volume so there is no concern of convection and the conductive properties of air are very poor.
Why do I need insulation in my walls if air is such a good insulator? Because your walls are not air-tight and there are large volumes of air in there, so you are subject to Free Convection displacing air and then the non-airtightness pushes warm air out and replaces it with cold.
