Since there doesn't seem to be any problems with actual scheduling and how much time you get, it does seem pretty foolish to ask him to close the relationship, at least when doing so comes from a place where you think it is going to address a concern you are having . Your comments typically sound like you know better than to take an irrational approach to solving your insecurity problems, so this post sort of seems out of character, at least from what I've read of the words you share on the forum.
There is nothing wrong with wanting to close your relationships, so it always kind of irks me when people need to mention all the "wrong" attributes of monogamous viewpoints, all of us get decide how we want to live, it's up to each of US as individuals and whether or not the people we choose to be in relationships with decide to accept the love a person offers.
There really isn't any reason to buck any style of relationship that people choose to live, you don't need any excuse to exercise the freedom to choose how you are going to have intimate relationships. The whole "this way is right" and another way is "wrong" is for anyone to say except for in our lives. If one of the reasons a person is non-monogamous, is because mono people have try to own each other, you might want to think about a reason you are polyamorous without having to justify it. There is absolutely no reason to justify your relationships by identifying how yours are right and someone else is wrong. Choose what you happy in life. The poly is right and mono is wrong attitude is the basis for the reason why people have to struggle just to be themselves, as the world is just now beginning to start taking a serious look at holistic civil rights.
I firmly believe that anytime you attempt to address problems in your life or relationships that have an element of denial in your planned solution will end up causing problems -- and not ultimately solving anything -- but rather compounding the issue. And if there is a real issue, solutions that started with denial will make addressing the issue successfully later on even harder because you are already making the root of the problem more hidden when your game plan is to go the easy route.
Anytime we justify the more "convenient" point of view simply because we don't feel like really addressing the issue, it is just going to ultimately add more dissatisfying aspects to your life, so I would take an honest look at what is really bothering you, and sometimes that takes many attempts to do. It's good to set the thought down and come back to it later so that your self-reflection happens from different emotional states or moods, at least that is what helps me be more honest with myself. It really isn't easy to do, and it is a practice, when some part of life feels dissatisfying to the point where you are thinking about taking action, make sure you identify the real problem and choose a more effective way to deal with it. Addressing the real issue will always be better for you in the long run. Sometimes you get lucky and the effective action is convenient, you just don't want to be taking the easy way out when it may not be as related to the problem as much as you initially believe, our emotions can get US to lie to ourselves if we aren't paying attention.
So take the time to figure out exactly what feels wrong or is making you insecure, sometimes it doesn't even require action, just don't get into the habit of solving problems by not addresing the issue, it's the same thing as feeling the need to be "correct" and "right" about the style of dynamic you choose to have in your relationships in your life. You don't need any excuses or reason to justify how you engage others, it is OK to do it your way simply because you feel like it.
But you'd be doing yourself a favor if you knew the real reasons behind your emotions, as that enables you to understand authentic emotions as opposed to training yourself to fool yourself
You don't have to be "right" or "correct" you just want to find a way to live that you know without any doubt will leave you content and satisfied, and that can be anything and anyway you choose, whatever you identify that makes you genuinely happy to live, along with those who choose to share their life with you