I'm not sure where we got the notion that readers have to identify with the main character. We are one of the most narcissistic societies of recent memory but we are still interested in people other than ourselves. We do still read about characters who are interesting even though (or even because) they are not like us.
I think there are four kinds of appeal a character may have for the reader: fantasy, aspirational, ideological, and representative.
The fantasy character is the one we wish other people were like: the Bond girl, the romantic lover of a romance novel. They don't represent reality; they feed our appetites. We don't want to identify with them, we want to possess them.
The aspirational character is the person we would like to be ourselves. James Bond, or the heroine of a romance novel. We identify with them in the sense that we want to think we could be like them.
The ideological character represents (at least figuratively) something we would like to be true about human beings, even if it is not. This can be negative as well as positive. Many portrayals of businessmen in fiction are ideological hatchet jobs. They appeal because they confirm our prejudices.
The representational character represents a genuine truth about the human condition. They appeal to us on the basis of recognition or sympathy. If we are narcissists, we are interested only in the representation of ourselves. If we are not we are interested in the representation of others. However, my guess would be that most narcissists are more attracted to aspirational or ideological characters than to truly representational ones. They prefer a magic mirror to a real one.
Which of these is better is an ideological and commercial question as much as an artistic one. Indeed, which of these is your prime consideration is likely to guide your answer. Artistically, representative characters should presumably appeal. Ideologically, ideologically compatible characters are presumably to be preferred. Commercially, fantasy and aspirational characters are probably the most reliable sellers, along with those that support the popular ideology of the day.
As a writer, I aspire to create representative characters. But I am aware that fantasy, aspirational, and ideological characters are likely to creep into my work based on my own fantasies, aspirations, and ideologies. I'm also aware that this is probably not the most commercially viable choice to make.