If it helps to know this, the best relationship I ever had (thus far) was a long-distance "romantic friends" arrangement. We knew each other as friends for years before getting involved, so we weren't the loves of each other's lives, but we had such a great connection in so many ways (including sexually) that we decided to give something more-than-platonic a try. I'd had relationships only with abusive men prior to him, so it was refreshing to finally have something healthy with someone reliable and respectful. And who doesn't like healthy companionship or sex with a respectful partner? ;)

For us, it worked because we were genuinely very good friends, which meant we were open, honest, and vulnerable with each other. (Not sure what you mean about "privacy," but no relationship can be healthy indefinitely without open communication.) We both made clear that we didn't see ourselves headed for marriage together, but we also just loved each other deeply and admired each other as people. So we didn't make long-term future plans, but it was still enriching. At the same time, we were happy to be monogamous, since neither of us was in a chapter of our lives where we wanted to go actively searching for a life partner. And the long distance allowed each of us plenty of personal space whenever we weren't in the middle of a visit.

So yes, this is possible. But you both have to be really honest about exactly what you want, to make sure both people are on the same page. ;)

I wish you healthy, enriching connections!