Well that "ish" part is rather significant reason it took Ducati 15 years to win another world title.
The single tire that everyone gets was optimized for Honda and was a disaster for Ducati. They had to get those engineers to reinvent the bike to make it work with those tires and still be a Ducati. This goes back to 20 discussions already reviewed on Ducati designing a bike needing a tire with a flexible carcass and tough tread as it always had a brick stiff bike with 'engine as stress member,' part of the fame and insane torque. Honda wants a stiff carcass / soft tread, going with super flexible frame, softer power delivery. Ducati chewed those tired and spit them every race and couldn't turn anymore because there was no more 'last-inch' lateral suspension from the tires.
Here's the math:
Honda sells 19,000,000 bikes a year
Ducati sells 55,000 bikes a year, and puts Pirellis on them.
Who's going to get what they want?
Michelin wins every race. Win on Sunday sell on Monday. If you only win 5 races a year (because Bridgstone was winning the other 20) you're not going to pay for your MotoGP dev costs. Put Michelins on a few million new Honda sales and you've covered your MotoGP dev costs.
This is why the single tire rule in a prototype manufacturer race.