As others have said, I don't think it's possible. I think Microsoft could gain some trust by bundling Chrome and Firefox with Windows, and possibly even abandoning IE, but I think that's fairly unlikely.
[edit] their best bet is to make the browser 'go away' so you can't even tell when you're in IE. I think they're actually taking steps towards this with the 'metro' version of the browser in Windows 8.
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As others have said, I don't think it's possible. I think Microsoft could gain some trust by bundling Chrome and Firefox with Windows, and possibly even abandoning IE, but I think that's fairly unlikely.
[edit] their best bet is to make the browser 'go away' so you can't even tell when you're in IE. I think they're actually taking steps towards this with the 'metro' version of the browser in Windows 8.