While rap/rock crossovers generally suck, your dream of better ones is within reach. I think the main problem with crossovers is that it usually involves a band that is so tapped for talent or creativity within their field that they have to start appropriating pieces from other genres, which isn't always a bad thing. however, without a proper frame of reference for the genre they use, it usually doesn't turn out pretty.
However, when it is someone who does the work of the middleman, taking the good parts from two different genres and putting them together, it works out great! There are all sorts of "mashups" now, but The Hood Internet is the place for you if you want Radiohead in your mixes.
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I think that the only thing that can make a collaboration between two very different artists work is if neither artists are actually involved. In your example of "Let Me Blow Your Mind," I think if it had been either Eve or Gwen Stefani (yuck!) calling the shots, the track would have been much different. Instead, it was a third party that was only interested in the results, which I think managed to keep the whole thing afloat.
You mentioned the decent-as-a-novelty Judgement Night soundtrack (at least it was better than the movie!) but I think a more telling example would be the Spawn soundtrack. Some of those "collaborations" were excellent, but the worst of the worst (Metallica, I'm looking at you) were so bad because of the one sided creative process.
When there are two very different artists working together, the only thing that will make a smooth, effective track is that niether one has total control of the creative process.
