I wonder if Eton would follow - why do I get a feeling they are so entrenched in their old ways, they would not.
Perhaps because you know naff all about Eton?
They have experimented with girls in the sixth form (ooh matron!) on and off since the 1970/80s. A friend of mine, daughter of a housemaster, was part of the experiment and gets very annoyed when people don't believe that she went to Eton for part of her schooling.
Ultimately they decided against it, but I know they do regularly review the situation. Tony Little put forward a very good argument for continuing as single sex, and I have to say I agree with him, although when my son was there girls did come to the school for certain lessons in the sixth form, as well as for drama and music, and he is still good friends with one of them!