It would be difficult to have enough replacement rainwater on hand at all times to be able to do large water changes. Most people with a hard water supply but soft water fish use RO water, either buying in the RO water, or have their own RO unit. Then the tank can be pure RO water, or a percentage mix of their tapwater and RO.
It's one reason we suggest people aim to keep whatever species will suit their water supply, or to ensure they can get RO water if they live in a hard water area but want soft water fish. Takes more knowledge about pH, GH, KH and other aspects of water chemistry to get it right.
If you use rainwater now, how do you manage during long dry spells without rain?