In response to the OP's question, I think that we already have relationships like this!...Thanks to the internet!
Sure, when the couple finally meet it may end up in a relationship with sexual love. But the weeks/ months before the meeting consists of pure chat (except for those cyber-sex people, lol) Now don't get me wrong, I know that there are weird creeps who deceive people online but there are a few gems out there.
I know of a couple who met in a chat room and talked for 2 years before they met. The bond between them was sickening (lol) in a lovey-dovey way. They are still together. Basically their relationship was based on friendship firstly, and has blossomed into a strong conventional relationship.
So could these relationships exist? yes. But not for long because instinctively we need personal interaction and sex.
(Sorry to quote Dr OZ, but the four needs a human has is food, water, air, and sex. Forgive me if I'm wrong with the quote, but it was along those lines)
My most serious relationships have always started with friendships first. Several of my best and closest friends through the years have been guys...but only a couple of those became more intimate. But I could never live with those guys who remained purely my friends. That much intimacy wasn't going to be good for our friendship.
So my bottom-line answer...I'm an ugly ducklng, too, although I'll never be a swan. (And I think she looked prettier before the transformation, IMNSHO.) And I still wouldn't have a relationship on this footing.
I don't understand how people can seriously say that he respected her?? He didn't respect at all her natural need to be loved in a sexual way, kissed and hugged, seen as beautiful and sexy by her husband, the man that supposed to love her the most. He was self-obsessive jerk.
Of course the long married couples sometimes don't feel the need for frequent sex anymore, but kissing and hugging and other signs of affection are always part of true love and respect. I didn't love the movie at all, it felt so contrived and implausible.