Generally it is not impurities or more so too many minerals of a certain kind. Usually not dangerous in any way. Providing it meets certain standards of course. Not disagreeing what you say but is too generic.

Treating water I have taken an interest in the production. You will actually find totally demineralized water tastes bad and actually is dangerous from a long term health perspective. You can buy it easily enough and it is entirely safe to drink but to most people, the lack of any taste is not acceptable. Soft water is also a complex term. You are rather correct in that you want a certain level of softness but this generally is to help in washing and to keep pipes clean. It does not necessarily help in taste and say in private well systems, you often will see soft water directed to the showers and toilets and hot water but drinking will be the non soft direct water. The soft can taste horrible.

Point being you really want minerals in water. Certain minerals anyhow. The exact make up of this will vary region to region so people may get use to some particular taste and not like another. Water with zero minerals will generally be universally not liked and somewhat unhealthy.