Breeder reactors are not used because refining the bred fuel costs more than processing mined uranium. The overarching requirement on fusion neutron absorption

Breeder reactors are not used because refining the bred fuel costs more than processing mined uranium. The overarching requirement on fusion neutron absorption material, besides delivery of heat to process steam, is that it needs to produce more tritium to burn. You don't get that if the neutrons are absorbed in something other than lithium.