Microsoft would love to, but they can't afford it. Bing is already losing huge amounts of money, and doing yet another deal for market share isn't going to be popular within MS unless it is profitable.
While MS could make money on a Firefox deal, they can't nearly make as much as Google can simply because Microsoft can't monetize the users as well as Google can.
You can see this on the demand side - many people try out new keyword advertising campaigns on Bing because they are so much cheaper than on Google.
Once they are confident they have a good set of keywords, they switch straight to Google (and at best keep the Bing campaign going). They'll pay more at Google, but get so much more traffic it is worth it.
Do you think Bing could be monetized at a similar rate to Google if their market shares were similar? Or are there other things Google are doing (e.g. better add targeting) that is making them more money per search?
Hard to know. Google does have better targeting at the moment.
Back when Yahoo was a player they built a platform that was supposed to match Google (Yahoo Panama[1]) that was their big hope of matching Google. It didn't succeed.
While MS could make money on a Firefox deal, they can't nearly make as much as Google can simply because Microsoft can't monetize the users as well as Google can.
You can see this on the demand side - many people try out new keyword advertising campaigns on Bing because they are so much cheaper than on Google.
Once they are confident they have a good set of keywords, they switch straight to Google (and at best keep the Bing campaign going). They'll pay more at Google, but get so much more traffic it is worth it.