Cellular, or foam concrete, is an intriguing option for a cavity wall fill. The lightest density offered in 0.18 MPa equivalent to 26 psi. At 28 days it can go up to 0.3 to 0.8 MPa or 43 to 116 psi. That doesn't sound like much but in the world of concrete and steel units are of a different magnitude. In wood, units are pound per square foot opposed to pounds per square inch in concrete and steel. That is an immediate factor of 144, 144 square inches in one square foot. Data is uncertain about the R value of the lightest cellular concrete but should come into focus quickly.
The reduced insulating cost over using polyiso is large. A 4x8x3" sheet of polyiso is about $50. The sheet is 8 cubic feet which is $6.25 per cubic foot. Regular concrete at $200 per yard is $7.40 per cubic foot. With cellular concrete one keeps the water cement ratio at 0.5. A 47 pound sack of cement at Home Depot is $11. That will make about 10 cubic feet of cellular concrete so its cost is $1.10 per cubic foot. It pours directly into the cavity without any cutting or processing. Filling the cavity eliminates air infiltration which can be overlooked at peril when dealing with insulation performance.
Its specific heat is 0.18 Btu per degree F per cubic foot. Consider a 2,000 square foot house, a ranch for simplicity, and deduct 50 sf for walls etc. Give it a height of 8', so the volume of air is 1,950 x 8 = 15,650 cubic feet. Its heat content is then 15,560 x 0.18 = 2,808 Btu's per degree F. Code required air changes per hour can vary from 0.35 from the Ashrae bible of required ventilation, all the way to 5 as recommended by the Center of Disease Control. Take an average winter day of a high of 40 and a low of 26. Average that to 33 to maintain an interior temperature of 68. That temperature differential is 35 degrees. In 24 hours the air changes are 24 x 0.35 = 8.4. So 35 x 8.4 x 2,808 = 825,552 added Btus just to keep up with the infiltration or ventilation heat loss. The average BTU of forced hot air is 80,000. To not get more complicated it's easy to easy that fresh healthy air is quite an expensive commodity that can be a hidden cost especially when considering "affordable" housing. Wood and drywall are about a zero thermal battery so the furnace turns into a real workhorse.
The point of this convected heat in most houses are is extremely expensive and inefficient. More about this in Cozycrete Thermodynamics.