Spring is nesting season and because turkeys are ground nesting birds, they're extremely subject to nest predation. While turkeys are relatively abundant currently (with some states having population declines worthy of note), it wasn't that long ago that they were almost extinct. It took a lot of money and effort to bring them back to abundance. Toms contribute to the nesting process only by breeding hens and one Tom can breed multiple hens. But hens have to actually hatch the nest and raise the poults.
There are some states that do have fall turkey seasons, and in those cases they do often allow hen harvest. It still has to be managed carefully but the fact that they aren't actively nesting in the spring helps limit the population damage that fall hen harvest does.