In English, it might be a gendered term, but in Swedish "hen" is a gender-neutral pronoun - and it's just been officially added to the dictionary. It's taken a while to get this far, though - the term was first coined in the 1960s but failed to catch on.
What about the prospects of such a pronoun in English? As Gary Nunn underlines, it's not as though there haven't been efforts to introduce one - more than 100, in fact, over the course of a century. It's just that creating a term is only a fraction of the battle - getting consensus on a particular term and propelling it into common currency and usage is a much more significant challenge. Language usually changes and develops organically, so to try to do anything in a prescriptive or deterministic way is problematic.
However, Nunn concludes that a unisex pronoun would be desirable, and not only for socially/politically progressive reasons. Speaking as a copy-editor/proofreader, it would thankfully remove the need to use one of those two painfully grammatically unsatisfactory options, "he/she" and "they".