Cost of living being expensive is due to national government inability to handle housing, infrastructure, etc and so forth. The EU does not dictate housing policy in member states, for example.
If the population is stupid enough to misunderstand the role of the EU and the role of their own national government, and prefers to listen to retarded propaganda that blames the EU for all their woes, then they deserve the hardship that will follow as much as they deserve being angry.