Yes, and no.
You are talking about receiving an ATSC signal in a car, so a new receiver is needed regardless of polarization.
But the idea would have to piggyback onto existing broadcast infrastructure. I have a hard time believing the broadcasters would want to reinvest - there would have to be enough demand to justify the cost. This where the OP's question progresses - multiple broadcasters sharing the load - and a evaluation would have to be done.
Vehicles and home audio equipment are almost exclusively already outfitted with vertically polarized receive antennas. While it would be easy to put an additional antenna in homes the problem is for mobile reception.
The beauty of vertical polarization is a vertical whip receiving antenna is omni-directional - this is great for mobile devices. With a horizontal polarized signal, the existing receiving whip antenna (vertically polarized) may still receive some signal, but it is so weak as to be impracticable. A second omni directional horizontally polarized antenna would be required for the receive end. And it should be placed outside the vehicle (cost), due to the partial Faraday cage effect. I have a hard time seeing the auto manufacturers justifying a second antenna for an unproven technology.
A circular (dual) polarized transmitter would potentially overcome this need for secondary receive antennas, but the wasted power, and the RF hazard at the tower base would be show stoppers.
I would think the issue would be better addressed when a mobile OTA standard is finalized and then use that.