I agree with LittleSara--my first thought was that your wife might be the one desiring a poly relationship. Maybe SHE has been harboring feelings for her friend? Maybe she's dreaming of a committed threesome relationship?
Or, alternately, maybe her friend has been harboring feelings for you, and your wife knows it and wants to let her friend be with you?
Regardless, the biggest benefit of polyamory that I can think of is that, if there were more than two people in a marriage, there would be more than one person sharing the burden of caring for the spouse who is ill.
When I see a spouse shouldering the whole burden of caring for their very ill partner, that's when I tend to think, "Monogamy is not enough for the demands of real life."
By the way, please don't forget to tell the friend that you actually are not at all interested in a sexual relationship with her. The subject had already been broached with her, and she was open to the idea, right? So she might be hurt if you don't follow through. Please tell her what you wrote here: You don't miss sex, you miss sex with your wife.
And now a totally different interpretation:
Here's what I think. I think your wife is not able to be EMOTIONALLY intimate with you right now (let alone physically intimate). And I think it's perfectly reasonable and okay for her not be able to provide you with emotional intimacy right now.
Your wife is experiencing physical disability, mental changes, personality changes, emotional changes, (probably) fears of mortality, fears of being a burden on you forever, and a whole lot of other stuff I can't even imagine.
Perhaps she simply needs to be emotionally and psychologically alone to deal with all of this?
Especially the personality changes--she has no idea who she is now. She needs to get to know herself, on her own, before she can provide you with the emotional intimacy you crave.
We tend to think that emotional intimacy is always good and always necessary. We feel that if people have a problem with emotional intimacy, they need to deal with it and fix it and learn to communicate better.
That's not always the case. Sometimes people need to go through something on their own, internally. I think that can even sometimes be healthier, more realistic, and better proof of psychological resilience and self-sufficiency.
This is a bit of a grim example, but I'm reminded of the Jewish tradition of being alone on your deathbed--the practice of turning your face to the wall in your final moment, to be alone with God. (I'm not Jewish, so forgive me if I totally got that wrong). That is meant to be a deeply religious moment, but as an atheist I always interpreted it as the need to be psychologically alone, to find peace with yourself.
On a much less extreme note, I have a chronic jaw condition that causes me pain periodically, and I prefer to withdraw and be alone when I'm having a flare-up. I just can't stand to see people upset at how much pain I'm in--it's hard enough just managing the pain myself. Having someone trying to help me DOESN'T help me. I can get through it better when it's just me and my body and my mind.
Sometimes emotional intimacy is just too much of a burden to keep up, or too much of a demand to ask for.
There's really nothing wrong with that. Especially since it will probably get better eventually, with patience. Be there for your wife, help her physically, and stop making emotional demands of her. She's dealing with her own emotions right now--she doesn't need yours on top of that.
I don't mean to sound harsh. But it does sound like your wife feels she can't meet your needs right now, but that it's not really your sexual needs (which aren't that important to you), it's your emotional needs she can't meet.
Maybe you would consider developing emotional closeness with the friend, so that you have someone to talk to intimately, maybe even do non-sexual things with like cuddling or even just going to the movies, to help yourself cope better?
Some poly people have more intimate (non-sexual) friendships than mono people do, simply because in traditional monogamy, you aren't really supposed to be deeply emotionally intimate with anyone besides your spouse. But that puts quite a burden on one person, doesn't it?
Single, straight, female, solo, non-monogamous.