ebook-meta can only do whatever calibre GUI can do in send-to-device/save-to-disk, and the only formats that support cover metadata are EPUB and AZW3. For example, MOBI can have a cover image file at the head of the ebook, but as far as calibre knows it is just the first page and there is nothing identifying it as a cover. (That is why you end up with 2 covers when you convert.)
A conversion will always prepend a cover, and for the two supported formats will add/update proper cover metadata, but for other formats will merely prepend the only thing that format understands -- a part-of-the-book image.
Which is why ebook-convert was able to add a "cover" (at least, we the reader know it is a cover instead of any random image).
Some reader programs, like the Kindle, will assume an image that is the first thing is the cover.
Basically, metadata support was a mess until EPUB (and it isn't wonderful even now).
I do not know why the lit didn't have the title updated. Does lit support metadata? I don't know, I never used it.
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