It depends on the file and how the cover was added when the book was created. My recommendation is run it through Calibre, add the cover in "Edit metadata" and then reconvert to .mobi. That should embed the cover so it shows up in Cover view.
Yeah, I've had the exact same experience. For what it's worth, I've also found a lot of variations between different editions of the same book -- at least for free classics that I'm downloading from the Kindle Store or Project Gutenberg. Sometimes it's actually worth downloading another edition, just to see how they implemented their artwork for the cover.
Every once in a while, I'm able to find a new edition where the cover artwork actually comes through!
It might matter whether you are loading onto a Paperwhite or Kindle Fire. On the PW, Calibre will allow the PW to show the cover if you add it to the metadata area in Calibre. I believe it even works if the book has DRM (and you don't have to break the DRM).
It is indeed a problem with some sideloading methods: even if the cover is in the book correctly it will only get transferred correctly if you send to your Amazon email address or use Calibre's "Send to device".
Personally, I use the built-in website in calibre - browse to it wirelessly from my Kindle to my PC - and covers don't get transferred.
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