To clear up some misinformation, this article points out that in Papanicolaou’s clinical trials beginning 1939:
"The researchers diagnosed 179 cases of cancer, 127 of which were cervical cancer. Nearly all the cervical cancer cases were invisible to the eye and visual inspection of the cervix and would not have been discovered without looking at cells under a microscope."
Cervical cancer is nearly always not discovered by a GP looking at a woman's cervix. Other gynaecological cancers or conditions may sometimes be diagnosed because of visible cervical or vaginal changes, but those are, I believe, usually symptomatic in other ways (e.g. pain, unusual menstrual bleeding etc), and usually only affect older women.
So these days, with HPV being all that's tested for, not cancerous cells, there's probably very little reason to have a smear test unless you're experiencing any symptoms you'd like to have checked, or are at higher risk of any other gynaecological cancers. Although of course, if you don't mind a smear test, there's no reason not to!
Also, self-tests don't require the cervix to be touched - you just have to insert the swab about 4-5cms deep, and move it around the vaginal walls gently but thoroughly for about 20 seconds. It's very simple. This can either be done at a GP's office behind the curtain (what I did at my last test) or apparently at home.
As for rates of cervical cancer in countries where self-testing is now the norm, I'm not sure, but I do know that in NZ, so many women who had avoided smears for years chose to do the newly offered self-test, that the system was swamped. Short-term chaos, but long-term a good sign, I think.