I can't see what the big deal is. Do people even understand the fundamental principles of this method and what the net effects are? Once you get to the bottom of what's physically happening in any method you'll see that there are ways to cut to the chase.
What is mineralization? From our perspective, the quick and easy explanation is that it is the conversion of organic forms of Nitrogen and other elements into an inorganic form which plants can use. People talk about "organic fertilizers" all the time, but that expression simply means that the initial form of NPK+traces is in a once living form. Amino acids, proteins, leaf matter and manure are all composed of complicated organic structures containing the nutrients elements. Plants cannot feed on any organic molecule. The molecule has to be broken down and the nutrient element has to be converted to an inorganic form.
Proteins for example, are very high in Nitrogen. A protein molecule is a huge complex structure with N intertwined. In order to get at the N the protein molecule has to be disassembled. This happens normally through bacterial action and the protein decays to form some other molecules plus NH3. Later, other microbes will Oxidize the NH3 to form NO3. This is the process of Nitrogen mineralization.
So what's the big deal? This is the same story we already know about. The plant can either use the NH3 directly, or can wait for it to be nitrified into NO3.
You can mineralize organic sediments by freezing and thawing or by high temperature methods. Baking your compost breaks down the organic molecules in exactly the same way as when you cook things you are going to eat. This kills the bacteria in the sediment and oxidizes the ammonia quickly, so after a few hours the soil is "mineralized". After cooling, the bacterial populations will rise again.
You can also simply dry start your tank for a few weeks. With plenty of Oxygen available and a moist soil, the bacteria in the sediment will mineralize the soil for you. So all this complication is really unnecessary because at the end of the day all we are accomplishing is the movement of NPK from one form to the other. Of course I've oversimplified things just so you can see the basic framework. Mineralizing the sediment beforehand means that you short circuit the need for Oxygen to be pulled from the sediment later on in the tank to complete the circuit NH3->NO3, so that is a good thing. Also, mineralization avoids the toxicity associated with NH3. Using compost is also a lot cheaper than name brand fortified sediments. So there are plenty of advantages, but keep it real. Do you like the look of compost? Does it fit with your aquascaping and maintenance goals?
I won't even go down the route of accusing people of being paranoid about water column dosing. At the end of the day, as someone else mentioned, this approach is very similar to the ADA method of lean water dosing and high nutrient content sediment. Aquatic plants don't really care, as long as they get fed.
What I don't like is this method being pitched as some kind of revolutionary technique that will save people from themselves. Just because the proponent shows a fabulous tank using the method, it does not automatically mean your tank will be fantastic. If you still make mistakes such as too much light or poor CO2 then none of this will save you from poor plant health. Since 95% of problems is related to CO2 we should not look at this as some kind of panacea, it's just an alternate method of nutrient delivery, and if you don't like working with soil or compost then you can achieve the same results with simple clay substrates fortified with Osmocote or any nutrient product, or you could get just as good results using any gravel and just dose the water column.
Cheers,