Sexual problems and mismatches are common in relationships, but this seems less a sexual issue than your gf's need for unrealistic markers of 'certainty' and validation from you. She's using the hypothetical promise of sex as some sort of reward for you making her feel emotionally fulfilled, which strikes me as a really immature and unhealthy approach to a relationship. Her sense of self-worth, self-confidence, etc. has to come from within herself, or there will always potentially be something making her feel insecure about herself that requires 'fixing' by an external source. What if you are married a few years and it becomes "but if I even catch you glancing at another woman, it makes me feel unwanted"? Or, "I won't feel truly chosen unless you want to have kids with me?" Or, "If you really valued me, you'd buy me/let me buy this thing I want"? Or whatever.
Re: sex... as a woman who has been through radical fluctuations of desire for sex AND responsiveness during sex, I can tell you that for me, sexual interest and responsiveness is 70% driven by purely physical factors (e.g., hormone levels, health issues), and 30% by outside factors (stress level, state of my relationship, etc.) I've had a previously strong sex drive/responsiveness turn off like a light switch b/c I went on the pill, or b/c my hormones were otherwise out of whack (with zero other changes in life, happiness, partner, etc). So I'd make 100% sure that there isn't something physical driving your gf's lack of sexual interest. You say she was originally interested in sex. Does that mean she was truly physically 'into it'? Did she get actively horny? Did she orgasm? Or did she just do it for the closeness/out of obligation, etc., early in the relationship? Does she still have sexual desire that she satisfies other ways (e.g., masturbation?) You need to be clear on this b/c if this is a physical thing, then fixing that might take the issue completely off the table. In other words, she might be interpreting her lack of interest in sex as a mental thing, when it is in fact completely physical in origin.
Going years without sex or sexual desire when one is otherwise healthy and one's hormones are not artificially jacked up indicates either some notable psychological issues around sex OR simply that she is mostly asexual or has an extremely low sex drive (which is perfectly fine, but would make her an unsuitable marriage partner for you).
But even if her lack of desire for sex IS 100% due to what she says it is, we are right back to my original point (see first paragraph).
My fear is that you are both falling prey to over-weighting your sunk costs in terms of time and emotional effort, and mistaking these for evidence that you are a good long-term match. People change over time, often A LOT. Many people on this thread have already commented about the challenges of failing to end relationships when they should be ended, b/c of comfort, logistical and financial convenience, etc. The problem is that so many people later look back with regret not on the relationship itself, but just on the excessive time and energy they spent locked into it.
I know someone who just went through this. Got involved around age 20 with a young man, whom she sincerely loved. Sex was fine in the beginning and the relationship was fine, if not terrific, for the first 5 years or so. But then she decided to go to college. He did more or less what he'd done since high school. They began to grow apart. Sex life stagnated, they began to fight about longstanding but previously less important issues related to their long term goals. They went to therapy and things would improve for a little while. They had shared finances, families, pets. But they never shared a long-term vision for the future. And their sex life gradually became nonexistent. Soon, 15 years had gone by, and they had spent roughly half their time together living as cranky roommates. He was still playing video games most of his time off, still working the same types of jobs he had right out of high school, with no ambitions to buy a house, save for retirement, or do anything else. She had a Master's degree, a budding career, and wanted to move along in adulting. They fought a lot and resented each other, but just couldn't bring themselves to cut their losses and end it.
Finally, my friend walked away. By that time she was in her mid-30s. It wasn't that she didn't love her ex, but he just was not a suitable life partner for her. And she knows that he never was, and she was too conflict averse to face up to it earlier. He was suitable short-term partner for the carefree days of their early 20s, and she bitterly regrets that she didn't have the vision and strength to end it 10 years earlier when she could think of relationship as a good one, instead of a tar pit she should have ended long ago. It could have saved them both 10 years of unhappiness and self-doubt, and also opened up 10 years of opportunities to find more suitable long term partners.
Don't be my friend. Those kind of regrets are hard to live with.