Of course more market share is good. But Microsoft is not purely interested in growing share with Bing; non-differentiation with Google is a good thing in and of itself. The less differentiated Microsoft is from Google, the greater perception of their platform having feature parity with Google. That way consumers are not forced to choose based on features, just ecosystem.
This is a the reason that Microsoft is a fast copier of market leaders, so that everything consumers could want, on paper, is housed within their roof (and Google's). It seems counterintuitive that less differentiation would be useful, but I think it's what Microsoft is going for.
Microsoft used to be able to "embrace and extend" in order to extinguish the competitor. With Bing it seems they can only "embrace", by which I mean copying and trying to decrease differentiation. But look at the trend. In the future, when/if Google search incorporates social feedback effects (ala +1), Bing won't even have the user-base to be able to copy the competitor, let alone extend and extinguish.
One look at my website statistics tells me Bing is already as good as dead.
I'm not completely convinced that Bing lacks the user base to compete with Google. There are diminishing returns in user base volume after some point, and Bing has around 100mm US users[1]. I think any of us would be pleased as punch with that volume and it's not clear it's not enough to do something-social-with-search.
This is a the reason that Microsoft is a fast copier of market leaders, so that everything consumers could want, on paper, is housed within their roof (and Google's). It seems counterintuitive that less differentiation would be useful, but I think it's what Microsoft is going for.