Not really relevant to your overall point, but I found it interesting that apparently F1 already tried that:
In 2005, tyre changes were disallowed in Formula One, therefore the compounds were harder as the tyres had to last the full race distance of around 300 km (200 miles). Tyre changes were re-instated in 2006, following the dramatic and highly political 2005 United States Grand Prix, which saw Michelin tyres fail on two separate cars at the same turn, resulting in all Michelin runners pulling out of the Grand Prix, leaving just the three teams using Bridgestone tyres to race.
In 2005, tyre changes were disallowed in Formula One, therefore the compounds were harder as the tyres had to last the full race distance of around 300 km (200 miles). Tyre changes were re-instated in 2006, following the dramatic and highly political 2005 United States Grand Prix, which saw Michelin tyres fail on two separate cars at the same turn, resulting in all Michelin runners pulling out of the Grand Prix, leaving just the three teams using Bridgestone tyres to race.
[1] https://en.wikipedia.org/wiki/Formula_One_tyres#History
[2] https://en.wikipedia.org/wiki/2005_United_States_Grand_Prix