I've had 3 colonoscopies,1 MRI, & have been to spas and never wore, nor was ever offered paper shorts. I wore my regular shorts for an MRI, & was always nude under a gown for colonoscopies, with all women staff (my preference as a straight male), and was always cool with the exposure. I did an online search to see what exam shorts look like, and i see there are a variety of styles, some of which look like they'd be a MedFet's dream.
I would suspect the purpose of paper shorts resulted from continued concerns got overall patient modesty, along the lines of a male wearing a paper gown during a physical for a male physician (you know, like "why?"). I think the paper shorts, like the gown, would be to standardize that everyone is allowed the same modesty & is covered the same.across the board. The modesty for physicals would be particularly for rectal/prostate exams, and perhaps for being weighed on a scale (since paper is very light). I tend to think moreso in terms of procedures rectal in nature (Colonoscopies, rectal/.prostate exams) where the front side genitalia need not be exposed, but is, & also too, to at least minimize buttock exposure which might help some patients who should have mental reservations about having such exams & procedures due to their concerns of modesty to the point where they would tend to avoid having them done, especially for something like a colonoscopy where you're typically "out" for the procedure, thus making you more vulnerable to what may be done to you
Also there wouldn't be any concerns over shorts coming in contact with the floor during a physical when they are dropped. Then there may be procedures where it's easier for the physician to just cut them off....