Regardless if it becomes the next evolution of the President's Cup, or a new standalone event, a mixed Cup would be a fantastic edition to the golf landscape. I could envision an event where day one would have Women's Fourball and Men's Foresomes, day 2 would be Men's Fourball and Women's Foresomes, Day 3 Mixed Foresomes and Mixed Fourball, and finally day 4 is singles (MvM & WvW).
We have enough recent examples of mixed professional events, concurrent professional events, and professional events in sequence that I would not be concerned about a course being setup well for both groups. In actuality, an event like this may tap into a classification of courses that has been bypassed by the Men's tour. Leading to a place like Cypress Point potentially being an idea venue.