If done right.... removing EVERY gobbler EVERY single spring will not affect the population. Sure, you'll never kill anything older than a 2 y/o bird, but it won't affect the population one bit.
What IS killing our population is that we are trying to remove every gobbler every spring IN THE WRONG WAY... First, jakes must be outlawed- they are required to fertilize eggs the following spring. Only approx 20% of jakes are sexually mature their first spring and capable of successfully fertilizing hens. So we cannot rely on them to fertilize hens after the adult male segment of the population is removed. Second, gobblers CANNOT be removed before hens have established nests to ensure maximum fertilization of eggs prior to setting. Sure, one successful mating CAN result in fertilized eggs up to 2 weeks after mating, but fertility declines very rapidly after 7 days of mating. And the more mating with more gobblers helps ensure an increased genetic diversity as well as improved fertility. It would also be nice if a gobbler remained available to service hens that are forced to renest due to predation. It is not uncommon for a single hen to produce as many as 80 eggs in the spring if they need to... I'm up to 24 from one jenny so far this year with my pet wilds, and the 3 of them haven't showed any sign of slowing down at all.
So... in other words... the population is actually controlled by the number of females (assuming gobblers ARE allowed to fertilize all available hens capable of reproduction (most jennies in the wild are not going to nest their first season) ). Since turkey reproduction and flock expansion are population INDEPENDENT (which means that, unlike deer and many other mammals in which the fertility of the animals decrease as the population increases and reaches carrying capacity), there IS NO maximum carrying capacity for turkeys.. you simply CANNOT have too many. Sure, there is a social carrying capacity- what the general population is willing to tolerate (farmers HATE them at time of spring bean planting or winter wheat planting), but there is no BIOLOGICAL reason to ever remove a hen from the population.
For those reasons, I have LONG been a proponent of pushing season opener back to mid April. This will allow most adult hens to successfully mate and establish an initial nest before gobblers are killed. I would also advocate elimination of all jake harvest in the spring except for juveniles to ensure there are adult males in the population to fertilize hens the following year. Furthermore, since there is no biological reason to remove hens except in cases where the population exceeds social carrying capacity, I would eliminate all hen killing except in cases of crop depredation or nusicance cases.
As far as spring limits go, I don't feel terribly strongly on the matter if the above changes were implemented. Personally, I'd favor a reduction, mostly because it would allow more birds to reach full maturity and 'trophy' status, but the population would do just fine with the above changes and remove all limits on spring gobblers completely.