The whole issue of covers in epubs is a murky one, if my understanding from previous threads on this is correct. This is again perhaps something that Idolse could answer way better than me. Certainly it would be nice to be able to check for books with a cover and books without a cover. I think the problem is the definition of what is a "cover", as commercial epubs could have some filename that doesn't look like any of those you suggested.
I do 100% agree that the ability to remove (or in my case add if not present) a cover would be useful without having to go down the conversion route. There are occasions where I get concerned that an epub -> epub conversion may "harm" the file in some other way particularly if it has never been subjected to such a conversion previously. For example making sure that it doesn't resplit pages on headings etc. I just don't know enough about the voodoo that happens when you hit convert to know whether with default options set it is anything to be concerned about or not. Undoubtedly there are people who have posted in the past about Calibre "messing" with their epub in some bad way in some particular situation but whether that is a now historical bug issue, user error or something else I have no idea. The whole "Tweak Epub" feature allows you to (manually) make such adjustments or fiddle with the css of course.