You are right, it is not usual to show a patient the inside of her intimacy.
In the 90s, some precursors considered this possibility but I remember one of our masters who said “Do you believe that after such a spectacle, these women will want their husband to enter there? » .
It is certain that the gynecologist must first view the appearance of the mucous membranes and make sure that nothing is particularly repulsive.
In recent years, in France, midwives have obtained competence for gynecological follow-up and they have adopted the habits of obstetricians. It is, in fact, quite common for a pregnant woman to be shown the evolution of her cervix during pregnancy using a mirror.
Personally, I don't regularly ask women to share what I see through the speculum. On the other hand, if we do a colposcopy, I do not hesitate to suggest that they comment on the video image. It is always easier to reduce the stress by explaining a possible gesture (biopsy for example) or by showing the absence of any worrying lesion.
As far as husbands are concerned (very few of whom come to the examination room in the end), it is first necessary to ensure that the wife is completely in agreement and to limit what could turn into voyeurism. Of course, we do not distribute photos as during a fetal ultrasound.
I am absolutely not against personal or couple explorations. Today there are many ways to buy a speculum on the internet. On the other hand, I insist on the need for perfect hygiene and the essential decontamination of instruments.
As for the site http://www.beautifulcervix.com/ I know it, it is a good way to teach the public to discover anatomy and understand the changes during the cycle.