It doesn’t take up much memory at all, but that also depends on file format, bit depth and size in pixels. UVs are set to be 1x1, or square, in some cases where this is not possible, some software won’t recognize the UV, (I had this problem not too long ago with RenderMan I believe) if the image did not fit 1x1 for some reason.
So is this a waste of space? Yes and I cringe every time it happens. Can it be clamped? Well not really, it’s coded like that and for a reason. There is actually a potentially infinite grid of 1x1 squares where the image is tiled, which can be helpful in some cases. SAving on texture memory can be done by knowing the application or the visibility of the object and adjusting resolution to those requirements. If it is something small or seen in passing, or in the distance then a low resolution map may suffice, close ups and high detail areas or large UV maps could benefit from 4k or higher resolutions.