You can of course leave any organic medium out of your soil mix!
This is how lots of vegetables etc. are grown professionally, even many bonsais.
However, you will have to modify your fertilizing and watering scheme accordingly:
- Water thouroughly, typically daily. Do not just wet the substrate, but have the water flow right through the pot. This will also flush out any surplus fertilizer and prevent the substrate becoming salt-laden.
- Fertilize regularly and heavily, typically two to four times the amount prescribed. Liquid fertilizers are easiest to use for that purpose.
This will work with all kinds of inorganic substrate, from stone-wool to lava, pumice, clinoptilolite, crushed bricks, … and lead to fine, healthy roots.
Also make sure, that your mineral substrate does not contain any dusty fractions, e.g. by sieving or intensive flushing before planting. No particle should be less than 2-3 mm in diameter. A good size for small pots is approx. 4 mm, for large pots 8 mm or even some more.
If you insist on using organic material, you might also try a compound, which does not decompose too fast, e.g. crushed pine bark. Coir does decompose rather fast, especially, if it is fine. This will clutter up your substrate in time, which is suboptimal for the root system due to the fine roots not getting enough air.