The "free market" option sounds great to begin with but it very quickly turns into a money battle and becomes very expensive for the tyre manufacturer who wants to win and for any team that has to buy their tyres to keep up with the team with a sponsorship deal from the best manufacturer. Not many tyre manufacturers these days are prepared to get into that kind of financial battle. Not all of them were even prepared to get into the bidding war for the WRC contract. If there was some way of making all teams source their tyres on the open market rather than through deals with the tyre makers it might work but even then how do you ensure that somebody doesn't get tyres with "trick" compounds to give them an advantage as has happened in saloon car racing in the past.