I did this Friday, but right at the end of work and we got off early, so I went home and never got on the internet this weekend. There is a harvest report floating around on the internet that the TWRA posted. It goes through 2011. The disclaimer I will add here is the #'s don't always match what comes up on their website, from 2006-2011. There are slight variances in the total kill #'s (+/- 30-50 birds in a given year). However it is what we have to work with. It starts in 1990 and some counties didn't have a season then.
Here is a graph I put together. I think the issue there became an issue when the limit went to 3. The kill #'s were already sinking for the most part, when it went to 4.
That being said, I don't think the TWRA has the workforce to do a bag limit, for each county, so I don't know what can be done other than either closing the season, for a couple of years or doing units, like they do for deer, which of course will just bring people from the lower bag limit units to the higher bag limit units to shoot extra birds. I don't think that is a good idea, but it's gonna happen anyway probably. That big yellow box down towards the bottom is supposed to say "under the 3 bird limit..."