The energy released by FRBs are of the order of what the Sun emits in 1 year not 1 day (assuming that FRB emit energy isotropically and that the distances estimated from the dispersion measurement of FRBs are correct).
Each burst lasts only a few milliseconds. What does the energy consumption look like assuming the FRBs emit RF directionally and aim at plausible targets in their sky? That's what an attempt to communicate would probably do.