Two of them, are added mainly for the nitrate (NO3) and phosphate (PO4). N, P, K(potassium) are some of the important elements that plants need to grow (macronutrients). Another one is C, added mainly as CO2. Plants need all of the macro and micro nutrients to grow, add only nitrogen(N), and potassium(K) and no phosphor(P) or carbon(C) and your plants will not grow as well. I will publish an article on this very soon and will keep you posted.
As you rightly say all of them also add K.Only very little from KH2PO4, enough for most aquariums from KNO3. Now the question is do you need to dose K2SO4 (potassium sulphate) ? Depends on your aquarium/plants. My suggestion and experience is that dosing more K does not hurt. If you follow EI why not follow it all the way to see the results of "unlimited" nutrient levels. Then you can play with more or less as you have a fair comparison.
By trace I guess you also mean Fe, so that is covered. You also need a source of CO2.
A high GH does not always mean you have enough Mg, Ca in your water. Check your local water report for estimated ppm. GH only measures Mg+Ca. Some observed improvements in certain plants after using the GH booster, but as you say it is not required as we expect the tap water to provide enough Mg, Ca, Cl etc.