dunno:
What purpose would a mixed Touro (Brooklyn) serve (not as if it will ever happen)?
As others have pointed out, if one wants to go mixed, they can go to a CUNY school.
it is difficult to argue that it is an absolute halachic prohibition for men to be able to see women during the service.
Very old Machlokes HaPoskim, with the origins being what and why the Ezras Nashim did in the Beis Hamikdash.
Satmer & Hungarian Poskim hold there was a visual problem as well, Rav Moshe (as Dr. Hall pointed out) among others, held it was a separation/reshus issue only.