This wouldn't be the first mechanical sport to change out tires at the end of a match. Some even change part way through!
https://www.youtube.com/watch?v=wZAw8cG9ZKs
It could get expensive to use them every match... which is why some of the racing sports limit teams to the number of tires they use in a season. However you can purchase various durometers of Urethane at resin supply shops, so there is no reason you couldn't design your own wheels, or a mold for the AM wheels, and re-cast your own tires when needed.
In fact I'm off to cast some mini-sumo robot tires right now...
Jason