Foam padding in case a good idea?

I'm thinking of installing foam padding such as those in the picture below.

The top foam pad is thinner and the bottom one is thicker obviously. I'd have to cut them to size and would probably have enough to cover once side of the case from the inside.

Would I benefit from any sound dampening effects? I'm not happy with one of the fans that I installed (marketed as silent, but is anything but) and I don't even have my GPU installed yet which will also create some noise.

How would my foam compare to something that's marketed towards sound dampening such as this? Do these even work?

Would my foam ruin the air circulation in the case?

My foam here.