I wish it had done, but I assumed the reason it didn't was because the original play that it is based on didn't really either, and using that as a scaffold they didn't think "what do modern UK audiences (as opposed to those of C18 Italy*) enjoy in a play with cross-dressing in? Oh yes, gender-queer flirting.

*Actually, they surely enjoyed some gender-queer flirting in their drama, too, if opera is anything to go by, but I don't know anything about earlier Italian stage plays.