Here's an argument that heat capacity shouldn't affect thermal conductivity in a solid: imagine a block of material with a smooth temperature gradient through it and the temperature at any point remaining constant, so there is heat flowing through it. Now imagine you have some tiny beads of some other material with a super-high heat capacity. Distribute those beads throughout the block of material, preheating each bead to the correct local temperature before inserting it. Then intuitively it seems that neither any local temperature nor the rate of flow of heat through the block should change much. Yet the heat capacity of the new composite material is significantly higher than that of the original material. Does that argument make sense? I did physics at school but not since then!

But in a gas, heat transfer is mostly driven by convection. Gas near the hot surface heats up, rises, moves to the cold surface, falls, and repeats. So what matters is the specific heat capacity * the flow rate between hot and cold surfaces.

Conceptually, it's like a thermos bottle, and you'd think that you would want a vacuum, but apparently that's hard to keep intact on windows, so a noble gas between the layers works better.

(While every noble gas has roughly the same heat capacity by mole/volume. Perhaps some CFCs would have been even better for insulation, but bad for the ozone layer, of course, and rightly banned?)