I understand where you're coming from. Years ago I had heavy, painful periods, I'd tried everything and even having two children didn't make any difference.
I wanted a hysterectomy and yes, I did go to the doctor and ask for one. It took time to get it on the NHS, although I could have had one and paid privately....at the time the cost was too much for us to afford.
I was sterilised first (keyhole) and then was able to argue that I wasn't ever going to have any more children in any case; also I had a long medical record of trying every sort of tablet to help with the pain, and also a good relationship with my doctor.
He wasn't impressed with my initial request, but did discuss it with me, he wanted me to be fully aware of the seriousness of the operation and the consequences of a hysterectomy. I'd done plenty of research and could discuss it intelligently, so they realised I was serious.
Eventually, they agreed after much sending to specialists and extra people examining me. I was married at the time so they insisted my husband was present at the discussions, even though it was my body, and he even had to sign to forms too....I felt it was wrong of them to expect that, but I didn't kick up a fuss as I wanted the operation.
I did have a hysterectomy, I can tell you it was the best thing I ever did. I never looked back, never had any dreadful after effects (although it takes a few weeks to fully recover after the operation), it freed me to live life again and even get a job, knowing I wouldn't be in bed for several days a month with dreadful pain/cramps/intense bleeding etc. I never had an early menopause (and I had a full hysterectomy, not a partial one) and have never needed to use HRT.
If you are really serious, do plenty of research, do go and ask, go through all the endless appointments and discussions and more discussions they will put you through....and eventually you will get it.
I was 34 when I asked for mine, so I was very young really, I am now in my 60s and still don't regret it, and I have never had any problems even now I'm older and well past the menopause. Good luck!