Depending on soil test results, P and K are usually available in measurable amounts and possibly, again based on soil test results, not necessary. In a lot of cases a big part of applied nutrients are going to be for the next year anyhow.
We also know tillage breaks down our soil, or more importantly causes the present OM to burn up faster allowing good microbes and worm activity to be reduced. Less microbe activity leads to longer breakdown times for anything in the soil. Tillage gets rid of the natural "glues" that bind our soils together leading to water and air infiltration restrictions that can directly impact nutrient movement through soils.
So if we have enough available nutrient, tillage actually sets back our soil health. Using tillage can have a negative impact as living organisms will help breakdown and move nutrients around in the soils. Disking at 4 inches still only gets fertilizers incorporated 2 inches deep, a depth that many nutrients can move on their own.