You're paying way more than just the cost of "a couple extra bucks... for detergents"! A 1/16" of scale on an electric water heater element can cost you up to 27% of every dollar you spend to heat water. In gas and oil fired heaters, it's up to 33% of every dollar. AND, there are many other hidden costs you aren't aware of, like everything you launder in hard water wears out faster, water using appliances and plumbing valves fail quicker etc..
If you'll check the label on your loaf of white bread, you should see about 120-150 mg of sodium per slice. A glass of skim milk is said to have 530 mg of sodium. The sodium added by a water softener is 7.85 mg/l, roughly a quart, per grain per gallon of exchange. I.E. 12 gpg hard water = 7.85*12 is 94.2 mg of added sodium per roughly a quart. So eat a sandwich less or drink less skim milk or give up a pretzel or potato chip and get on with life
And not softening all the water in the house may be okay, although IMO it's a dumb idea, but if there's iron and/or manganese in the water, who wants rust stains in their toilets and kitchen sink? The vast majority of softeners soften all the water to all fixtures in the house/building. That's the right way of doing it because then you get the benefits of softened water everywhere.
Water is either soft(ened) or hard. It can not be "too soft"; it's either got one or more gpg of hardness in it or 0 gpg of hardness in it; speaking strictly of residential waters, commercial/industrial waters in many cases require less then 17.1 ppm/mg/l (1 gpg).
Some people, although very few, add some hard water back into the softened water rather than get used to their skin's natural oils making them feel slippery while they shower in softened water.
The use of potassium or sodium chloride makes no difference in the softness of the water UNLESS the softener is leaking hardness because of the use of potassium chloride. In many cases you need a higher salt dose than sodium chloride requires; from 12% to 30% for high efficiency salt doses. Gary Quality Water Associates
formatting link