It might work if there was some signaling for the programmable SAME alerts, but that's a lot of headache to replicate existing infrastructure. Plus, if car radios all had VHF tuners for weather radio the reception would be much less choppy than trying to decode an HD-3 on the move.
But I guess a plain' ol simulcast wouldn't be a total waste of space, and certainly it wouldn't eat up much bandwidth. Back in the analog TV days, the Fox affiliate in Birmingham carried NOAA weather radio on their SAP channel except during Spanish simulcasts.