Soil wars: there is a huge range of strongly held opinions on potting media components. Any discussion is liable to bring on a flame war. However. I will try to touch of few more topics without getting people too worked up.
FIrst: every "formulation" of potting media requires a unique water and fertilizer program. If you understand how to water and fertilize your chosen potting media, you can very successfully grow a nice tree. If you don't understand the product you are using, you will be doomed to less than ideal performance out of a product or potting media formulation.
Many of the complaints around Akadama are due to the fact that we "Mericans" can not read Japanese. We often don't know what we are buying, if you can't read the label on the bag of Akadama. There are several grades, not only of particle size, but also degrees of hardness. Soft, Medium and Hard Akadama are the hardness levels I have "Been told about" because I can not read Japanese. I have had excellent results with "hard" akadama, even through our sub-zero Chicago winters. I have had terrible results with "soft" akadama, which can go to mush in one season. If you live in an area with below freezing winters, only purchase the hard grade of akadama.
Second, there is no "substitute" for Akadama. Its properties are pretty unique. There are many potting media formula that do not use akadama, but these are not "substitutes", they are simply different. It is best to think of akadama free potting media as simply being different. They require different watering and fertilizing. Just learn how to handle the mix you choose to use.
Sieves will improve virtually any mix. The more uniform your particle size, the better your potting media will breathe, the healthier your roots will be.
Humic acids, humates and fulvic acids are wonderful elixirs, and actually improve over time the structure your potting media. Humates can be obtained in seaweed emulsions products. Use humates as part of your regular fertilizer program and your potting media will survive longer without the need to be repotted, and you will have healthier roots.
In general, no potting media should be single component. If you use single component potting media, you pretty much are guaranteed to have problems. All turface, or all haydite, or all bark will cause problems. One exception possibly is all pumice. 100% pumice is the mix of choice for establishing newly collected conifers collected in western North America. It seems to work well.
Pumice is the single best component to be used as a part of a potting mix design. If you look at trees of high quality, at shows, you will find the vast majority have pumice in their potting mix. 25% pumice to 75% pumice is the common range. Pumice is great stuff. Difficult to source east of the Mississippi River in North America. Common in western north America.
Turface - this is a calcined (fired) clay. It is recommended by many as a potting media. The product website for Turface does not recommend using Turface as 100% component in potting media. The Turface website actually recommends not using it at more than 25% of a potting mix. Personally I have had trouble with any mix that is heavy in Turface. At moderate levels, 25% or less of a mix, it is really nice stuff. Some will not use it at all.
Horticultural charcoal - and or biochar - this is "good stuff", at bout 10% of a potting mix. Effect more than anything seems to be to encourage healthy mycorrhiza. If you can find it in the right particle size, use it.
Crushed Granite, Decomposed Granite and Crushed Quartzite - basically, inert rock. Holds very little water, mostly just adds weight to a potting mix, causes a potting mix to hold less water, dries out a potting mix. Recommended to not use as a "main body of the potting mix" component. Excellent for top dressing pots that are not going to be covered with moss for display. Some of the quartzite and decomposed granites have very natural colors that make for an attractive topping component to apply on top of your main body of potting media. If used in medium to large size bonsai pots, can quickly take the weight of a pot from a "one man" lift to a "two man required" weight.
Perlite - this is a man made product, quite similar to pumice in its chemistry and physical properties, but it is extremely light. Great stuff for a grow out container, especially if you are located where pumice is expensive. Use perlite instead. However, it is too light to use in shallow bonsai pots. So in nursery containers, perlite is great, in bonsai pots, use pumice instead. Perlite will leave your tree unstable and wobbly.