I asked my DH to have one. We've got two children, one with additional needs and childbirth amongst (not exaggerating) killed me the first time (ELCS for the second). I've been left with permanent injuries from the first birth and will likely in time need a hysterectomy. Doctors are currently reluctant to do it because of my age but that's going to be the end result.
I asked him because I can't use hormonal contraception and even condoms aren't infallible. If I accidentally get pregnant, I cannot carry another baby without huge risk to my health, and we don't want any more children anyway. It would be me that has to go through an abortion, which I would do, but I would really struggle with it.
It was affecting our sex life a lot because I would avoid sex because I was anxious about getting pregnant. He was getting frustrated because he wasn't getting any, but when I took the time to explain it to him he 'got it' instantly.
He was squeamish too, he didn't relish the idea at all! It's not a particularly pleasant thing to have done! But he booked in, saying 'I think it's time that I took one for the team now isn't it'. Yes my love, yes it is!
As soon as he understood, he did it. I won't lie I would have thought less of him had he not, it would've been incredibly selfish for him to expect us to carry on our sex life as normal knowing how I felt.
Snip done, tests clear. Normal service has resumed! It's not infallible obviously but he will do a private test every year to ensure it doesn't fail until I've been through the menopause (or had a hysterectomy) so we're as covered as we can be.
You're not unreasonable OP. We women give a lot when we have children physically and mentally. Whilst you can't force him, it's pretty crap if they won't do what is essentially a minor inconvenience for you.