No, what you're ignoring is every crop pulls off more nutrients than it has the ability to put back through decomposition. Even if you have two crops in a field or 100. The actual fruit of that crop pulls off nutrients. The vegetation from a tomato plant if it's plowed under or pulled off and put in a compost pile and reapplied only has so much nutrients. So that vegetation portion (minus the fruit that you picked) dies and supplies nutrients to a squash plant 3 feet away, ok. Is it enough to supply that squash? Maybe, because squash may have smaller nutrient requirements than tomatoes so what little goes back is enough. That doesn't help when the next crop to go in there or another crop growing next to it has a higher nutrient requirement. If tomato vegetation that is left to rot in the field puts 40# of P into the soil but the watermelon growing next to it requires 80# of P that other 40# is being pulled from the soil and eventually brought down over time or replaced via something. Compost can only add back the equivalent of what was pulled off if the compost included material from another source, outside of what was harvested.
Plants with longer root systems are mining nutrients further down, correct. And when they die those nutrients are available in a shallower portion of the soil profile, correct. That still doesn't account for the nutrient removal value by the fruiting portion of a crop, unless you're going to pick your tomato and then throw it right back down into the ground to rot.
The entire world imports potassium from somewhere, an overwhelming majority of the potassium comes from Canada, Belarus, Germany and China. China is the only one who's not a net exporter of potash, because of their growing agricultural sector. 90% of the potash used in the U.S. comes from Canada so we're not importing it from overseas.
It has nothing to do with how we've farmed our soils, it's natural chemical makeups that produce different nutrient balances in the soil. Positive nutrients stick to the soil profile, K, Ca, Mg, Na and H. The numbers of these nutrients in the soil are affected by parent material, that has nothing to do with human doing. Think of the soil as a parking lot, and it has 100 spots (everything in the soil adds up to an index of 100). If Ca occupies 90 of the 100 spots, that only leaves 10 spots for the other 4 positive ions I mentioned.
The soils of western KY and NW TN tend to have Ca levels in the 80-90 range. Why? Because the underlying parent material is calcium limestone. Over years of weathering and breakdown, this parent material has released Ca ions into the soil and they occupy more parking spots at the expense of K (potassium), Mg etc. Ideally your soils would have 3-5% occupied by K, 10-15% Mg and 65-72% Ca. This a "required" ratio for optimal yield, optimal mositure retention, optimal rooting ability etc. The soils in that part of the world have a makeup more along the lines of 1.5% K, 8% Mg and 80%+ Ca. Therefore, potassium has to be added to the soil to get back into optimal balance.
You go along the OH River in KY and their soils have Mg levels bordering 20%+ and Ca levels that are too low. Too much Mg creates a tight soil, which restricts root exploration, holds too much water to the point of saturation and crusts more easily in dry spells. Too much Ca creates a too porous soil and water retention is minimized. As a result of freer water flow through the profile, leachable nutrients such as nitrate forms of nitrogen, sulfur and boron, are more readily lost.