Burning is advantageous because it will return many nutrients to the soils, and give your PH a good kick in the right direction.

It does need to be done at the right time (like before seed heads on weeds are formed). Once they mature and fall off, many weed seeds will germinate anyway. The hot air rising will form a convection and pull the Heat upwards as opposed to under the grasses and many weed seeds will survive the heat, and can outcompete the native wanted plants to come back if the timing is not good. Check with your local biologists, especially the ones that are into birds, as they will know those grasses inside and out.