Is brine practical for home driveways?

Speed

No, because it takes a lot and will flow into lawns and garden beds, not only killing what's there but making it impossible for new plants to thrive until that soil is replaced or the salt in it diluted by lots and lots of rain or snowmelt. Rock salt works well enough and is easier to control.

CantHaveItBothWays

Maybe for rural driveways of sufficient length and maintenance. For most residential areas, it is not practical. There would have to be storage for the brine; would it be communal or private property? Everyone who uses it would have to have a way of aplying it. That would involve fuel and storage. Everyone who applies it would have to know how to apply it, how much, when it is appropriate to use it,and what happens to the environment.