I think this is a great idea. Most of the concerns were valid, but I'd like to provide some perspective. Crushing the biochar is work that you have to do anyway, and it makes it better biochar by having more surface area. I do agree with covering it with wood chips, mulch or soil. I also wouldn't put it right next to the house, I'd put it out a ways. That way, your shoes are brushed off a little bit before you go in the house, even if you wear shoes inside.
I think it especially works well if you have completed most of the most crucial biochar areas of your garden area. Rock won't do for you, half of what biochar will do. It doesn't sequester carbon, it doesn't provide housing for microbes, and it certainly doesn't absorb water for dry spells when needed.
I live in the Pacific Northwet, so it might work better in an area with a lot of moisture. Alternatively, you could of course mix it with compost or soil first, before you add it to the paths. It will really retain moisture then and be unlikely to dry up and blow away. Most people inoculate their biochar in one way or another, as it has been advised by the "experts" for some time.
I am looking forward to seeing the results of your experiments, William! The way we learn things is by someone like you coming up with an idea and trying it. Sometimes then adjusting it, or inspiring someone else.