You can’t filter out ions of calcium like that. A huge reverse osmosis system for the entire home would be prohibitively expensive. I used to live in an area with very hard water and everyone had water softeners. You only need to buy the salt every few months and it’s not too bad. RO filters were only connected to a tap on the side of the sink in the kitchen - those membranes aren’t cheap.
RO also puts about four times as much water down the drain as it filters. A whole house RO filter is extremely wasteful. You don't need to be filtering every toilet flush.
Yeah, I think most people, myself included at one time, are more fascinated by RO than we understand the practical considerations.
Use RO locally at a single tap in the house, if the water quality warrants it. Perhaps add a desalination unit before the water heater, or centrally if you have some very hard water. But a central RO? Sounds expensive.
I've considered a central RO for prepping purposes, but even then a gravel/sand/active charcoal filter, followed by a UV-C mercury lamp, would probably be more cost effective, and easier to maintain without access to replacement membranes.
You are technically right that the water heater softens the water a bit by precipitating the minerals around the heating element and thereby removing them from the water. But that is energy inefficient and expensive, since you normally don't use a water heater to soften your water but rather to get warm water. So putting another system in front of the heater that softens it first is better than replacing the heat element every so often.