My basement was finished, probably in the 1970s. There are 1x3s nailed to the concrete block exterior walls with wood paneling attached to the 1x3 strapping. There is no insulation. The concrete blocks are lightly painted with something black, probably roofing tar for waterproofing.

This basement is not damp (a big reason I bought this house). No leaks or water damage in the basement, I live on a hill with well drained soil, so I'm not worried about moisture.

I want to replace the paneling with drywall for a more modern look. There is currently wall-to-wall carpeting, which I want to keep.

I was thinking of putting 3/4" rigid foam between the 1x3 strapping and sealing around the 1x3s with spray foam. Then I would attach drywall to the 1x3 strapping. By doing this, I would not have to mess with the carpeting.

Is there any benefit to adding the rigid foam? It's not much R-value, but the walls would be sealed. Our winters are mostly below freezing (Dec-Mar). The forced-air heating keeps it warm enough, but would adding this small amount of insulation make it a bit more cozy in winter? Or is it not worth it? In other words, will it make a noticeable difference?

Any other thoughts or ideas about how to update the walls?