Consuming less is definitely a big part of climate plans I've seen. Consuming less doesn't have to mean a reduced standard of living. This article mentions heat pumps for example, which consume much less energy. Other plans I've seen also include supporting dense development (=consuming less land/resources for housing), supporting public transit (=consuming less energy for transportation), and upgrading efficiency in homes (=consuming less energy for housing). I think longer term, the cuts will have to be deeper due to population growth, but there is so much low-hanging fruit.
I think in general the environmental movement has been hurt by the association with austerity. Most people don't like being told their lives have to get worse for a benefit that's difficult to see. It needs to paint a positive vision of the future that people can get excited about.