I'm not sure how much it would help balance the herd based upon what's getting shot. I think there are many hunters who won't shoot a doe and hold out for a buck no matter what, so many may well not take part in an early doe season. We've got neighbors like that.
It might help with herd management from a stand point that bucks would be given a couple weeks warning before people start shooting at them with firearms. Guns going off in the woods can make deer nervous. But if it happened too early, then the woods would have time to settle down again.
I know we have ample opportunities to take does during the regular firearms season and following muzzle loader season and we don't shoot them because we take our does during bow season which is about two months prior and about two months following gun season. Shooting a doe with a gun isn't much of a challenge on our property. So we probably wouldn't participate in an early doe season using firearms anyway.
My only objection would be that in Missouri bow season closes when gun season starts, so I'd lose a week or two of bow hunting during the prime part of the season. Other than that I'd have no objections to an early doe season. I think it might be one of several changes Missouri is considering.
Here is where Missouri appears to be headed, take note of the graphs as the table can be misleading.
I'd say changes are in store for us.