>> I think the hydrogen peroxide would kill off the good microbes too?
I would mostly expect it to kill equal numbers of "good" and "bad" microbes, but really the most it can do is reduce their numbers. Fertile, living soil has something somewhere around millions or hundreds of millions of microbes and spores per cubic inch. (I might be off by 100 or 1,000 either way, so take it with a milligram of salt.)
After all, almost one billion bacteria can fit into one cubic millimeter, and there are 16,000 cubic mm per cubic inch.
I figure that there is no such thing as "sterile" outside an operating room, Say you kill 99% or 99.9% of every germ in that potting soil. There will still be thousands or hundreds of thousands.
Maybe it just levels the playing field so that the natural advantage that plant roots give their symbiots lets them outgrow the plant pathogens.
Peroxide does donate some oxygen to the soil, and for some reason beneficial microbes tend strongly to be aerobic.
I forget if I've said anything against MR mixes above, but I don't want to speak against them. I think they're a great idea.
If we give plenty of them to young plant roots or radicles, the root hairs will take up and encourage the exact species of root fungi or root bacteria that they are compatible with. (I didn't know there were beneficial rhizobacteria, but I guess there are, and now I need to memorize how to spell THAT!)
The only downside I can think of is that we tend to pamper seedlings, and the roots only take up the MR in large numbers if they are in arid or N-poor conditions. But the idea that they displace or fight off root diseases is exciting, and hopefully remains true even in moist, fertile potting mix.