Since we've past the peak of natural gas already in north america and importing liquid natural gas is a disaster waiting to happen (and unsustainable), we must find other ways to cook our food.
I think this is a great way to cook using all local materials, as long as you have access to clay to make the bricks! No need for imported metal cans for a regular rocket-stove or materials to build a solar oven.
Since small pieces of wood are used in a rocket stove, the wood can easily be grown by using the coppice method. Which means cutting down a tree and letting the stump re-sprout into multiple, smaller trunks. They then slowly harvesting your woodlot periodically in sections and as long as you do not cut down the tree too fast and let it grow and generate more stored energy, the stump will keep generating new sprouts for firewood!
I'm not sure how long the wood lasts and how often you have to add to the stove, but it uses much less energy than a traditional fire. It also does not need much space so this could be used in most if not all living situations. The only requirement is access to fuel, the community would need to have a dedicated and managed coppiced forest.
A more transitional approach would be to use an electric cooking stove and hope for power from 100% renewables or a new invention sometime in the future. But how much will electricity cost, could you depend on it, and will you have a job to afford it? Furthermore, as globalization becomes less dependable because of the peak in oil production it may not be easy to throw it away and buy a new one from the local corporate box store. So we need to ask, who will repair the stove or make a new one when it breaks? If a new one is made, what materials will be used, and how will those materials be mined using what kind of fuel... Maybe it's easier to just plant a tree.