The only reason they're thinking it has less latency is because they're only considering a point-to-point case.
Once you wire that up to the various hubs and routers of the underlying DSL or cable infrastructure, or try to send traffic to somewhere other than the end-point the microwave is connected to, your latency rapidly goes to shit.
Add in the fact that fiber can transmit over longer distances, the weather-induced degradation of most microwave links, the fact that the whole link drops when a semi-tractor travels along the highway between the two links when line-of-sight is close to the ground, the need for high and unsightly towers to get over the trees and buildings, and the final fact that microwave towers were decommissioned in Canada precisely because of all these problems, and all you can say is:
Bad idea.
Very bad idea.