Yes, they actually did. Females desiring sexual experiences was considered a form of mental illness, so some would go to a doctor to treat these urges. One mode of therapy was vaginal stimulation.
Krafft-Ebing, a 19th-century doctor and early sexologist, wrote about female sexuality as a perversion in his work Psychopathia Sexualis. Michel Foucault also reflects on the treatment of these women in his History of Sexuality.
And would it have been considered inappropriate for a doctor to treat his friends or relatives in this way, much like a modern doctor might perform exams and minor procedures on them?
As an addendum to what's already been mentioned, "Female hysteria" was seen as a catch-all term for a variety of different mental illnesses today (Clinical depression, Bipolar, Schziophrenia etc). It was thought that hysteria was caused by the uterus detaching itself & floating around the body causing women to react in an odd fashion. There were even adverts in newspapers showcasing the vibrator.
You're right to say that Richard von Krafft-Ebing thought of female sexuality as a perversion but so did many people in the 19th Century. Until Alfred Kinsey's reports in the late 40's & early 50's, certain people still thought the woman's purpose during sex was to please their husband. They never considered that women might also get enjoyment from sex. Even if they said well women experience "orgasms" it would've only been mainly to treat their hysteria. Female orgasms weren't a thing that was really considered in the 19th century. They weren't even called "orgasms" they were known as "hysterical paroxysms of relief".
Kinsey's Sexual behaviour in the Human Male (1948) & Sexual behaviour in the Human Female (1953) were eye-opening (especially the latter) in how we understand sex. Instead of using three categories (homosexual, heterosexual & bisexual) to describe men & women, Kinsey devised the "Kinsey Scale" as he thought that sexual desire was fluid; 0 - Exclusively heterosexual, 1 - Predominantly heterosexual only incidentally homosexual, 2 - Predominantly heterosexual, but more than incidentally homosexual, 3 - Equally heterosexual & homosexual, 4 - Predominantly homosexual, but more than incidentally heterosexual, 5 - Predominantly homosexual, only incidentally heterosexual, 6 - Exclusively homosexual & X - No socio-sexual contacts or reactions (what can be thought now as "Asexual" &/or "Aromantic").
However what's really interesting is the results;
Men:
11.6% of White males aged between 20-35 scored a rating of "3" throughout their lifetimes
50% of all married males had some extramarital experience at some time during their married lives.
Sadomasochistic responses (this is anything from biting to more extreme forms of S/M)
So that was the male results let's look at the all important female results, 19th Century Psychologists & Sexologists if they were to look at hypothesize the female results they'd probably put it at around 0. However they were wrong;
Women:
7% of single females aged 20–35 and 4% of previously married females aged 20–35 were given a rating of 3
2 to 6% of females, aged 20–35, were given a rating of 5
1 to 3% of unmarried females aged 20–35 were rated as 6
The average frequency of marital sex reported by women was 2.8 times a week in the late teens, 2.2 times a week by age 30.
1.0 times a week by age 50
26% of females had extramarital sex by their forties. Between 1 in 6 and 1 in 10 females from age 26 to 50 were engaged in extramarital sex.
Sadomasochistic responses;
A bit more info on biting, erotic responses & women:
Definite/Frequent ~ 26% Some response occasionally ~ 29% Never ~ 45%
Number of Cases ~ 2,200
Things to consider about Kinsey & these studies: Kinsey classified couples who'd lived together (whether they were legally married or not) for a minimum of a year as "married". This classification obviously affected the outcome of results somewhat. Also I think Kinsey only surveyed men & women who were born as their biological sex & not TransMen, TransWomen or those who identified as a different "gender identity" to their "sexual identity".
Kinsey also tried to challenged & IIRC supported some of Freud's theories on infantile sexuality & Psychosexual development. Evidence that supports this is the fact that Kinsey collected information on pre-adolescent orgasms (children aged 5 months & 14 years), Kinsey states that he collected the data through adult's childhood memories & adult or teacher observation. Kinsey also interviewed paedophiles who had sexual encounters with children who gave information on how they thought the children responded.
Sorry for the slight digression there but I hope you still found what I had to offer interesting :)
Sources & Further Reading:
The Technology of Orgasm: "Hysteria," the Vibrator, and Women's Sexual Satisfaction ~ Rachel P Maines
Psychopathia Sexualis: eine Klinisch-Forensische Studie ~ Richard von Krafft-Ebing
Kinsey el al 1948, 1953
Sexual Behaviour in the Human Male & Sexual Behaviour in the Human Female ~ Alfred Kinsey
An add on question to this, it's regularly posted on reddit that vibrators were originally developed by doctors to treat female patients with but i remember one time a redditor went through all the sources and found all went back to one single source, a book written by some random person. Can anyone clarify the reality behind this, did doctors develop vibrators for this purpose or is it just a myth?
There was a film about this but I can't remember the title - help anyone?
