It has been tried before, more than once. Here's a few reasons why rubber doesn't work well in 12th...

Weight - they weigh lots compared to foam, and this seriously affects handling and acceleration compared to foams.
Slip angle - IIRC, a foam tyre is like having thousands of little rubber tyres, all with their own slip angle. As a result, foam tyres still grip when they get to crazy slip angles, where rubber tyres don't. Once you 'lose' a 12th car on rubber tyres, it just flies straight off the track.
Cost - they would still have to have a foam inner to support the (extra) rubber tyre. Cost would be like now, plus the rubber tyre.
Grip - a rubber tyre changes grip as it wears, a foam tyre doesn't.
Handling - a key adjustment to 12th car handling is tyre diameter. This is easy to do, relatively cheap, and makes no change to mechanical grip with a foam tyre. A box full of different sized rubber tyres isn't my idea of travelling light, or lo-cost racing!

Last, and for me, by no means least, one reason I stopped TC racing because of the incessant tyre war. To lose out to people with $100s of tyres in their boxes, who tested them all and could have the right one, just p****d me off. I really don't want that in 12th. I buy four compounds and race everywhere. One of the great appeals of 12th is that you can buy all the technology used to win. RC12L4, Corally SP12X, CRC 3.2R and GenX, Speedmerchant, motors, cells, speedos, servos, etc, etc, - they are all winners and come straight out of the box. Can you get that in TC? No.