No, WMP is completely useless. No part of it is needed.
I love XPLite, but it's not perfect and when dealing with WMP is a perfect example. I've seen it screw up every time when trying to remove it. So, reinstall WMP, then type this in a run dialog box:
You may need to run it twice before getting rid of every file in the Windows Media Player folder (like if you updated WMP from an older version, for example), but it works perfectly.
RunDll32 advpack.dll,LaunchINFSection %windir%\INF\wmp.inf,Uninstall
Should work then. Well, you may want to reinstall a K-Lite Codec Pack, just in case. The Mega Codec Pack is awesome!
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