Wiley journals request payment from authors who want an image to appear on the journal cover. Is this a common practice followed by many publishers? Why do authors pay the fee?
It's not that uncommon. Authors pay this charge mostly because they think having a cover image increases their reputation and/or impact. I don't know any study proving this assumption. Please let me know, if there are any.
Nevertheless, if an author wants to have a cover image, I always suggest to negotiate because this significantly decreases the amount of money the author has to pay, see e.g.
Similar story: Journal (a respected one) offered to use one of our images for their cover page. They wanted $1800. I said I don't have the money. They offered to do it for $900. I said no. In the end they put it on the cover for "free".
Source: Tweet be @rauscherMRI
In my experience, it's not common. Much more often the front page of the journal is a rather drab-looking, standard page that the journal uses again and again with minor changes. If the front page does vary, it's decided by the editors, who also choose the image to feature.
As for why authors might pay the fee, this is a form of advertising: by having an image of their research in a more visible venue, it might make people read their paper. The page you linked gives some examples. The front page is used in marketing materials, on the journal's webpage, etc., and is likely to be seen by more people as a result.
I was told by a Wiley journal that my article image was being considered for the front cover. They 'asked' for a contribution of US$1400 to the publishing cost of this, but when I refused because our funding for that project is now concluded, I didn't hear back from them. So there appears to be no 'unbiased' selection process, rather this appears a quick money-grab from the publishers.
This is pretty shameful behavior, especially as to be 'selected' required time and energy to prepare the image for their requirements. Not impressed.