DLF, you came here asking for advice from people more experienced than you. Tinwen and I have both answered your words from that perspective. No one here has any ill will, and generally we all try very hard to understand. What we are answering is your words themselves, such as I've quoted above, which is all we can do. It is up to you to take the advice or leave it after that, but no one here offers advice in anything other than the spirit of helpfulness.
The quote above reads as, at least to me "I can't control your emotional side, so I'll control your sexual side, because I have to feel that something belongs to me." Wording says a lot about the person saying it, often without them realizing or intending it.
You may not read jealousy and insecurity into your post, but demands like "no sex" and wording like "shouldn't let her" are born pretty much of only that type of emotion. There is no positive, affirming, secure emotion that breeds such strictures (yes, there can be practical reasons for this, such as risk of STDs, pregnancy concerns, medical issues, etc., but your reasoning is strictly emotion based, as far as you've stated). Sexual exclusivity within a fully mono relationship isn't the same thing as "date and fall in love, but *I* control your sex life." This isn't a put-down. Pretty much everyone is jealous and/or insecure at some point and on some level. It's the work we do on *ourselves* to figure out the actual root of these emotions that helps us, not placing restrictions on others. Jealousy is often a very simple label used to describe very complex emotions, and it's pretty much always worth untangling those emotions and the causes of them, regardless of whether your poly or mono. It can only help you.
Yes, theoretically it could work. Theoretically, so can many things that, in reality, have very little chance of success. That doesn't mean you can't try for it, but it does mean you should both be aware and honest about what that actually means in terms of consequences. There is a small percentage of people in the world who are totally asexual with their romantic partners; and, while this is a totally viable relationship, the chances of that person also being poly, and attracted to your GF, and compatible with her, and okay with being totally secondary to you are just statistically incredibly unlikely because you decrease the dating pool tremendously with each caveat. You can both agree that is okay, and pursue that; but, know that it can also (and often/usually does) result in much unhappiness by pretty much everyone. It sounds like a reasonable compromise because it comes closest to making you happy right now, but you both should have an actual plan and a safe space to talk about desired changes for when things change and come up (because they will). Not doing so will have it's own consequences, which I listed above (resentment, broken promises, etc.).
Again, it is OKAY to be mono. Poly isn't any better or worse, it's just another relationship structure. But, if you are going to go down the mono/poly path, there will be a lot of self-work involved, too. What seems like a good compromise from the inside of what is, clearly, a very emotionally challenging time in your relationship is something we've seen here so, so many times before. Those veterans of the board who have experience in poly can really be helpful, if you'll take a deep breath and look at the posts with the idea that the responses are usually from people who have experienced and/or seen others experience what you are going through. Take some time and read some of those threads. Tinwen and I aren't warning you about pitfalls because we want to bully you into doing something else: we're doing it to help you avoid them, or at least have some idea how difficult it's going to be and to help you develop a plan for dealing with them.
