Although Michelin joined for tyre wars - some of them preferred having some competition and beating each other race to race. 1997, when Bridgestone came in, was a great tyre war year between Bridgstone and Goodyear, some races the Bridgestone teams would be battling away at the front even though they were teams like Prost and Arrows who didn't have competitive chassis and engines.
This was an even better form of branding than having the only tyre in F1, because it would make wins by a certain tyre brand more significant, and it would get drivers saying in interviews "wow those Michelin's were great for this race".
Some are even suggesting that Bridgestone made the tyres rubbish this year on purpose so that its a constant talking point.
Next year with the ban on refuelling and the greater focus on tyre management, a tyre war would spice it up no end.
However, tyre wars are very expensive and its just not sensible in the current climate.