Battery power for an oven like this is not necessarily cost-prohibitive; if you want cost effectiveness and long lifetime, LiFePo cells can be had for ~$60/kwh, which would be under <$200 for an ImpulseLabs sized oven.
Absolutely agree on resistive heating for cost effectiveness: Some cheap cells, resistive heating and minimal power electronics would probably be the way to go for the African market.
I already managed to ruin a pan with just 3.7kW (heated it while empty), and I tought that was a lot.
However, I think the cost is probably mostly the battery. Our induction hob (max power per burner 3.7kW / 7.2kW total) costs only 10% of the battery powered stove.
Also, at the low cost, induction is a non-starter. Resistive heating elements are dirt cheap, and the efficiency is not much less than induction. Induction is just way nicer :)