Why Can't Women Play Men's Roles as Frequently as Men Play Women's?

I stumbled across this casting call for Doctor Faustus on Playbill.com, and a fascinating document it is. It gives the salary for actors doing shows at CSC (not much), discusses how much double-casting they're doing, and gives hints of the tone the show will take.

Sarah Bernhardt as Hamlet

It also reveals, as so often happens, that the men get all sorts of interesting roles (devil, clown, doctor) with all sorts of interesting things to do. The one women, however, is to be "Female, 20’s. Vision of loveliness, incomparably beautiful. Sexy, pin-up girl. Possible nudity."

Yes, of course Doctor Faustus was written centuries ago, and that's a pretty typical role for a woman in those days. (And not even actually for a woman, since it was likely played by a man.) But it's the 21st Century, and nontraditional casting is one of the glories of modern theatre. However, that nontraditional casting is often limited to two types: (1) people of color playing roles that are not traditionally played by people of color, and (2) men playing women. 

For some reason, having women play men is a lot less frequent, but why? Why couldn't a woman play any of these roles in Doctor Faustus?

• WAGNER: Narrator of the play; A more refined and learned clown; Faustus’s servant.
• MEPHISTOPHILIS: A devil called on by Faustus. Depressed clerk who has worked at the same desk job for all these years.
• A clown; brazen fool, but not without native wit.
• Another clown / bumpkin; a complete idiot, innocence incarnate and a dupe; loveable and dangerously daft.
• The Devil; kind by temperament, but firm; likeable.
• An almost absent presence, like a wayward son or disaffected teen.
• Versatile utility actor, comedic clown.

It's not as though CSC has never had men play women. For example, in their production of Passion, men played women's roles. 

Passion, and also Peter and the Starcatcher (not a CSC production), to name just two, reveal that many people's imaginations only go in one direction. Directors and other creators can visualize men as mothers and nannies, respectively, but somehow cannot visualize women as soldiers and pirates, also respectively.

There are a number of levels on which female-based cross-gender nontraditional casting is important. It adds texture and variety. It gives the audience the pleasure of watching some truly amazing underemployed performers. And it helps them to have careers.