Interesting idea. Not going to happen, but interesting.
Several years ago I talked with a DNR deer biologist from another state. He believes their doe harvest declined - and I think had some numbers data to support it - when they expanded their "doe days" season.
Before, he said, there were only X-number of days for hunters to kill does. They knew that and targeted them during that period.
After expanding the days, hunters said, "Eh, I don't want to fool with it tonight." ... "I have to be at work by 10 a.m." ... "I have Little Johnny and don't want to mess with a doe today." ...
They put it off because there was no urgency. When it came time to "buck hunt" during their peak rut, there were no does killed. Then the season ended.
In effect, there was no dangling carrot to chase with the expanded seasons vs. the short period.
If you have four hours to mow the yard on Saturday morning before T-ball, consumes the afternoon, you don't mow on Sunday and then work all week ... chances are good you'll mow the yard.
I do basically the same thing now. I don't shoot does, probably been 5 years since I shot one and that was because the land owner in KY ask me to shoot one with my bow. I pass on a lot of them until one day I see one and every thing is right, not neccessarily rack size or age, I shoot him. The T ball problem went away more years ago than I like to think.