'Hmm... Although I've never been in a QPR myself, so I can't really know what they feel like, I feel like there might be some insight to be gained in defining why I don't want a QPR.
To me, I don't want a QPR because... I like to be my own boss. I very strongly dislike the idea of any sort of formally defined relationship- I can't be tied down to any one specific person (or multiple people, in the case of polyamory).
Now you might think this makes me a very solitary person, but I'm not. I love my friends. I love having very close friends, I'm very committed to my friends, and I would absolutely love to live with friends someday. So what's the difference? Well... Friendships aren't formally defined. They just evolve naturally, and can change in nature without it being a big deal. I feel like once you're in a QPR, though, then you're In a Relationship, you know what I mean? You can't be in a QPR with someone unless one of you brings the idea up and you both agree to it, and then after that you're Partners, and you can't change that without like, announcing it you know. (Obviously all QPRs are different and not everyone uses the same terminology, so please forgive my generalizations.)
With friends, you don't have to formally declare the nature of your relationship, and honestly you don't really have to do much of anything. Should you do things like keep in touch with your friends, make time specifically to spend with them, etc.? Sure, if that's the kind of friendship you have. But you're not obligated to. I am extremely committed to my friends and I like to go the extra mile to support them, have fun together, and make them feel appreciated, and I would absolutely never abandon my friends at the drop of a hat, but I like being secure in the knowledge that I'm doing it because it's what I want to do at any given moment in time. It's ok for friendships to change. You can be super ultra best friends with someone at one point in time, and maybe a few years down the line you two aren't nearly as close anymore, but you're still friends. That's ok! Friendships are loose and volatile and fluid, and that's what I like about them.
Hell, even my best friend... I've known her since I was four years old. We're super close, go everywhere together, we'd totally be willing to live together indefinitely. But even with her, I know that should we ever grow less close, there's no need to formally declare it. And I like knowing that I don't have to consult her on any life decisions I make- I might do so anyway just because I value her opinion, and I certainly wouldn't up and move away without telling her, but I don't have to. I can do whatever I want with my own life. I'm not afraid of commitment, I just dislike obligation.
Now of course, it's not like I can do everything my way forever. I know eventually things like roommates, etc. will become a factor in what I do. I also know that no two QPRs look alike, and not all may involve life partnership or a specific level of intimacy or anything like that. But in any case, to me, the thing that makes me feel like I wouldn't want a QPR- even if a theoretical QPR I could have might in all other ways seem identical to friendship- is the act of formally declaring a relationship status, as well as in general a sense of obligation to do things a certain way and share a level of involvement in each others' lifestyles.