I'm not seeing how Michelins problems at one race would prevent this? It's not like Pirelli hasn't had multiple races with issues of exploding tyres or concerns about it happening. Sure, Michelin might still be shy but it wouldn't prevent another company if the deal was right.
People always talk about the Pirelli claim of tyres lasting all race, which misses the point on both what I want for the rule change and Pirells statement. Tyres for race cars are a balance between performance and lifespan.
Do you really think that Pirelli could make an all out tyre that could lap at a qualifying pace for an entire race? It's not a cost free benefit, the tyres they talk about are going to be slower. Besides we still have the two compound rule, so it's pointless for the to make them.
Tyres that last an entire race would be slower than ones that do not. With out tyre competition it's the same for everyone so who is more kind on tyres, such as a team with bags of performance in the bank, has a big advantage in the race. With competition between tyres you can claw back performance at the expense of laps per tyre lifespan.
The current quali tyres often cannot even do a full lap flat out, that is pathetic and down to policy not tyre limitations as the policy for false competition has gone too far. It has also made the tyres too hard to understand for all teams and made the cars too sensitive to conditions.