Something is... off... here. Something is not adding up.
Does your wife have any history of trauma or being abused? Anything which might have impaired normal bonding in relationships?
My hunch is that she needs a visit to a doctor, for a thorough evaluation; physical and mental health. Hormone levels, thyroid, all of that, but also depression, anxiety, life history. There's a piece of the picture that's not quite clear in your posts.
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She does have some issues from the past (don't most of us?) and I do believe they have added to the problem. Her mother was very promiscuous when she was a child. She saw many men come into and out of their lives and 'learned' that sex with strangers is good and fun and didn't have any kind of role model with a stable father in her life. Her dad was married 6 times. And, sex was not hidden from her...she would hear it going on, even when friends spent the night with her and she was so embarrassed and grossed out by it. So to her, sex with someone she loves is 'weird' because she views love with me as she does love of a family member, not as a romantic partner. I am sure this contributes greatly to the way she views sex between us. To her, sex is only fun if it NOT with someone you love. When I try to explain that with a husband, you can open up and be yourself without any fear of being judged or rejected and we can learn what each other needs. She said that just feels too strange to her and that she doesn't like to get all emotionally close like that. Sex to her is better if it is somewhat forced, fast, unplanned, and with someone she doesn't have feelings of love for, just lust. Foreplay is out of the question as that leaves her mind too much time to anticipate or think about what is about to happen. I am basically here for safety, security, love, support, co-parenting, etc...sex is something that is for procreation or for people to do without love involved. Sex and love have nothing to do with each other in her mind and it's only fun if there is nothing deeper than physical and on the surface feelings involved.
So, after writing all of that, it does appear there are issues. However when I ask her is she would be willing to talk to a sex therapist the answer is always 'no'. She doesn't feel like she has any problem. Her sister is a huge alcoholic and this seems similar to me in that neither can admit there is a problem. They think they are completely fine and that me wanting sex is actually the problem. She can't understand why I feel a need for it with her, but understands logically that people who love each other do actually have sex. Also, we have had many talks trying to understand if there were some form of past abuse or something. Other than the obvious issues above with what she experienced growing up with her parents, there has not been anything with my wife herself. She was not physically abused or raped or assaulted in any way so that hasn't been something that plays into it with her.
It is hard because I feel like she does need to seek out some professional help, but she is unwilling to do so and does not feel like she needs it. I feel like her father more than her husband sometimes. I think she probably feels that way too.
Until/unless she seeks help, I don't see this ever getting any better. Do I stay and just provide her with that 'father figure' love and forget about any physical or emotional intimacy forever?