"Why is the pH of the water important if the alkalinity is close to nothing?"

Ahh, I get what you're saying. Time for the pool boy to come to the rescue! (Yup, did pools in Plano and Dallas, TX.) First, there's Alkaline-Earth and Alkali metals.

Alkalinity in water solutions almost exclusively refers to alkaline metal content. It has practically nil directly to do with pH, but it does affect it. Alkaline solutions are always basic, yes, but alkalinity is a separate test from pH altogether. Calcium and Magnesium are alkaline metals. This also imparts different chemical properties upon the nutrient solution which are better described by a 300-level college professor than myself. Such ions within certain balances will cause acidic conditions, though other balances have been known to cause suddenly basic conditions. It's a whole mess involving Newton's Third Law that even I am not qualified to explain. That's 600-level stuff.

Then there's Alkali metals, sodium, potassium, and (VERY RARELY) hydrogen (usually found as a dual-atom stabilization in nature, and often bound with oxygen to make water,) being the most typical ones involved in plant growth. These are not as often found (in fact very rarely found in nature) in a pure plant-usable form.

Typical ion filtration uses hydrogen-ion filtration with carbon filters - this produces almost soda water (you're only missing the gas/liquid ratio + pressure to have soda water) and this makes it very unstable. You must let it stabilize with the atmosphere, then add nutrients. Differing pH levels will cause lockout not only for absorption but also for proper solubility in water itself, so it can cause deficiencies as well.

EDIT: Think of it like this, as this is how we do in the pool industry; pH is POTENTIAL HYDROGEN. Alkalinity is the alkaline and alkali metal/molecular concentration. This has effects upon algae growth and such. Had to call my brother's father for clarification on this, as we both work together on making new hydro systems. Nice to have men with a common goal and engineering background to work together - he's the one that taught me about pools.