The short answer is yes(1), no(2).
The quantification of the power spectrum is performed via the Fourier Transform over an image. An image is a matrix that describes the distribution of reflectance (or radiation more generally) across the field of view of the camera. It therefore has only a remote "relationship" with what is actually depicted in the image (the physical scene). Image resolution and spatial resolution are two different things. You can use a 50MP camera at the end of a telescope or at the end of a microscope. Both images will have the same image resolution but they will be "looking at" different spatial resolutions (actual space being sampled).
In other words, small objects correspond to high frequencies and large objects correspond to low frequencies but what is large and small depends on the context of the image (and the characteristics of the imaging equipment to an extent). Consequently, what is "high", "medium" and "low" spatial frequency can only be expressed in relative terms and either with a lot of assumptions or constraints.
The approach of dividing the available bandwidth into three bands and estimating the average power in each is, of course, reasonable.
An improvement would be to take a set of representative images, average their spectra and look at the actual bandwidth they occupy and its shape with a reference to the actual objects they represent to then decide at a different possible assignment between the low, med, high characterisations. But this implies specific scenes with a specific field of view, orientation, resolution and any other factor that affects the recorded spatial frequencies.
In case it is of any additional help, there is a concept in image histograms called "Adaptive Binning" where, the width of a given histogram bin is not fixed. The width is decided after an optimisation process over a criterion and it is image specific. For example, one criterion could be that each bin should represent at least
N pixels. Although originally not defined over spectra, this adaptive concept might be useful here as well but applied over FFT bins. For more information please see this link.
Hope this helps.