Consequences of BPP=BQP
Assuming a practical algorithm is found, the applications will overwhelmingly be in quantum simulation. Basically any research in large quantum systems - chemistry, biochemistry, condensed matter, nuclear systems will be affected. We'd likely see major advances in basic biology, medicine and pharmaceuticals. Moore's law would be restored for a few years and we would finally have working fusion reactors. Physical simulation using the new algorithm might also lead to new physics.