There are modern already sites that IE fails to render properly, especially on the mobile side. Enough of them that microsoft has even written a guide to help you write portable websites:
There is some deep irony from fate, that when the world was full of "IE only" websites, "mobile IE" sucked and was unable to show those sites. Now that mobile IE is on par with desktop IE, and both are nicely standards compliant, both are having trouble showing some sites, as the world is shifting to webkit-only...
And with IE as the only browser for windows phone, IE has become one of the weak links of the windwows phone platform...