This is a nice informative video. I wish the creator would tell us his qualifications - though at the end he does refer to a source for his ideas - Living Web Farm (which I have not checked out).
He states several times in the video that crushing biochar is detrimental, and maybe he is right. But the high porosity of biochar is a microscopic feature which may or may not be affected by breaking up the char. In the related material, activated carbon, particle size is chosen on the basis of optimizing flow of air or water through the media, not because it has any effect on the capacity of the carbon to adsorb. So put a pin in that point - it may be inaccurate. Big pieces may take longer to adsorb AND release nutrients. The interior of big pieces may not be accessible to plants or fungi (though in the fullness of time the carbon pieces will break smaller and smaller).
Biochar is becoming one of the most common and discussed ways of CDR - it is so accessible to the average person in many variants. I suspect that in the long run, the means of making char will become much more sophisticated and the gas produced by pyrolysis will become a valued product itself - not something that we'd want to burn. But that is for another decade or two . . .