In a sense, yes, bonsai is almost hydroponics. I grow my bonsai in Turface MVP, a totally inorganic, high-fired montmorillonite clay that is marketed to sop up water on athletic fields. It is like coarse sand or gravel but retains much more moisture than either of those materials. In the opinion of many, the 'ultimate' mix is grains of lava, pumice, and a clay from Japan (Akadama) that is added for moisture retention.
One supplies NPK and minor elements via fertilizer. Some use liquids applied during watering, such as Miracid, and for these it is exactly as in hydroponics. I use Osmocote-Plus prills that release their contents, depending on temperature, to roughly match plant needs. So maybe this is even closer to hydroponics with a high-tech control system.
Roots require oxygen to live and grow. These bonsai substrates have high air-filled porosity. Roots also must be kept damp, of course. These substrates/mixes also simultaneously have high moisture retention. Wood chips and/or chipped tree bark are the best organic substrates, but they do break down and the air-filled porosity correspondingly reduces over time. These hard, inorganic substrates do not. Conventional potting soils also compact and cannot achieve the same levels of air-filled porosity and, hence, they become highly problematic in shallow pots.
One thing these hard inorganic substrates do that hydroponics and soft soils do not is produce root ramification. When growing root tips deflect around hard particles, they branch or ramify. Plants in these inorganic substrates develop densely ramified root pads that are highly efficient. The epidermal cell wall extensions called 'hair roots' occur a few millimeters behind the growing tip, so more tips = more water and mineral adsorption. Conventional hydroponics and growth in soils are missing this aspect.