EU severely reducing its fossil fuel imports from Russia in 2022 cut down natural gas usage by 17% and overall energy consumption by 3%. So yeah, increased price due to scarcity help a lot in shifting around the energy mix.

It's a bit shit that hits poorer people relatively more than richer people. Governments can reduce this impact by subsidizing sustainable alternatives (like heat pumps). It's still leading to inequality (unless you give more subsidy to the poor), but at least overall people will hopefully benefit.