You are governed here by the laws of physics and the only useful option to fill a standard height box is by using the cover value for the object-fit property.
If you use the value '
fill' then the image is stretched out of its aspect ratio and no use for real world images (unless its just a random shaped image). Images of people, places and objects have intrinsic aspect ratios which generally cannot be changed without distorting the image (i.e. being stretched or squashed).
When you use the value '
cover' then the image is scaled to fit both width and height while maintaining aspect ratio. That of course means that if the image is a different aspect ratio than the box you are trying to fill then the image must be oversized in one direction to fit and is thus clipped at that edge. There simply is no other choice if you want to fill a box that is a different aspect ratio to the image and have the whole box filled up.
If you use the value "
contain" the image will fit inside your box but it will not fill the whole box unless it just happens to have the same aspect ratio as the box it is placed in.
These are just the laws of physics and you can't put a square peg in around hole unless it is smaller than the hole or you chop off its corners