It does occur now. On the Dubai leg.
Across 2 fields and the men and women's are staggered across 3 days. Womens play Thu-Fri and men play Fri-Sat..
Women have the main field on Thu but are relegated to the second field on Fri, with only the women's Plate and Cup GF/SF been played on the main field.
Sure you could do this in Sydney with the women playing at the SFS on Fri and then moving to the SCG on Sat while the men play at the SFS..
But what is it that this actually achieves? the reality is that Friday would be a poor crowd during the day and then on Sat you have to choose between watching the men at the SFS or watching the women at the SCG.
If you watch the women at the SCG do you then have to go to the SFS for the women's plate and final?
I personally don't like the idea of multiple fields and shunting the women's to the SCG and making them play second fiddle to the men.
Hong Kong ran the Olympic qualifiers alongside over 3 days, however due to the structure of the women's Seven's means they also has more games with an extra 12 games of finals for all the various plate, cup and bowl finals matches that the qualifiers didn't play.