I think that trait, in itself, isn't all that attractive in a romantic companion. As part of a set of other quality traits, most men think its fine. A woman still has to be pleasant, supportive, fun, etc. Independence isn't a substitute for all that.
Like I said, men and women tend to be rejected for substantive reasons rather than shallow ones. Few women (or men) are truly rejected because they are too successful, have their act together, etc. They just aren't delivering on qualities the opposite sex finds appealing. Independence isn't a substitute for that in any way.
"I think that trait, in itself, isn't all that attractive in a romantic companion."
I agree.
I see nothing wrong in how a couple complements each other. It may be that one is very independent and the other is dependent. If it works and is only one component of many that makes the relationship positive then that's a good thing.