One original article from 2008 made the case that they suck up a lot of CO2: https://www.nature.com/articles/nature07276 (or https://sci-hub.hkvisa.net/10.1038/nature07276)
But this finding was challenged in 2021: https://www.sciencedaily.com/releases/2021/03/210325150055.h... (or https://sci-hub.hkvisa.net/https://www.nature.com/articles/s...)
Edit: Dunno if climate is really the best argument there anyway. The old-growths have high biodiversity value, and are hard to regrow. Carbon is more or less a fungible commodity that can be sunk in a billion other ways.