Random story: I've used Chrome since the day it was publicly released and am fully aware that the address bar does more than just accept urls - in fact, it's called the omnibox for a great reason. But I still type in "google.com" for 99% of my searches (probably 100+ times a day). The reason is that I like the Google homepage. The white space allows me to clear my thoughts without being distracted by whatever would be on my screen otherwise, and the search box is perfectly positioned in the center of my screen. Weird, I know, but I like it.
Interesting, I actually use Bing (or at least go there once a day) mainly to see a new picture every day. It's often high quality nice shots from random places, so I feel like I'm learning about a new place every time... makes me dream :/
This is one reason I don't mind that the only built-in option for search on Windows Phone is Bing. While I believe I get better results from Google (though that may be bias on my part), when I hit the search button it pops up a nice picture. Many times the picture is relevant to a holiday or special event that occurred on that day, and there are call-outs you can press to see quick facts (today's is about Yamuna River pollution and the Taj Mahal).
It's a good example of TheCoreh's point that it's all about providing a more compelling experience. If I was given the option when I first turned on my phone, I likely would have put in Google just out of habit. Today, I probably would not. Probably.