If the cover has creased, the layers of the paper will have separated and the fibres pulled out of alignment. The crease is then bulkier than the rest of the cover and stretched on the side it bends away from.
As you cannot push the fibres back into their former alignment, this is a technique I have used to get the cover to lie flat. Note, don't do this with a valuable book whose ££ you wish to retain, as it is ultimately a destructive method.
I started with this book (click images to enlarge):

Turning to the inside of the cover, I used a fine scalpel blade to 'shave' away the upstanding line of the crease.

I then used tape strips across the shaved crease to restore tension to the inside face of the cover. I would have preferred to paste paper strips, but had no paste available.


The corner will remain damaged, but looks better when sitting out and is less likely to sustain more damage when being returned to the shelf.