I met a potato farmer whose primary crop is for a large chain supermarket. He produces almost double his required yield, doesn't use fertilizer nor pesticides... and has been so for a decade. To use his words: he's a potato farmer, but spends most of his time preparing the soil for the next year. He's right into cover crops (ie not leaving the soil exposed), and several 'rotational' crops that assist in root and nutrient management, as well as pesticide control (yes, plants to control pests). These rotational crops are generally 'terminated' early by finely mulching them back into the earth while simultaneously seeding the next preparatory crop. His biggest expense, fuel, is reduced with a smaller tractor, which also assists in minimising soil compaction.

Yeah biochar is very interesting. We definitely shouldn't massively start using it in the short term though - its effects are not so well understood. Most "knowledge" is based on terra preta, Amazonian dark soil which is hundreds of years old and man-made with charcoal, pottery shards, bones and other organic matter. There have been field trials but many of them by biochar organizations/companies who might not be completely objective and once we put it in the soil we can't really take it out anymore.

I think the evidence suggests that turning waste into biochar and applying it to fields at a local scale has a lot of potential. Growing trees for the purpose of biochar might be a different story (this has many of the downsides of biofuel production).