Or better yet why isnt their a very long doe season in parts of the state with this problem?
That's the best question. The answer is, in many states, the regs HAVE caught up to the need, with extended doe seasons and other incentives to take does*. Sounds like NE is just slow on the uptake in updating their regs. The proper course of action is to sit in on meetings of the wildlife department and offer your input, and/or submit input in writing to the wildlife department. It seems a shame and terrible waste to just shoot them and let them rot, so I would ask both for a longer/special doe season, AND in the meantime, at least allow those with depredation permits to take the meat - what harm could that do, anyway? Write some letters, my man - the squeaky wheel gets the grease.
*For example, another way to incentivize hunters to take does is to restrict the number of bucks you can take. In this state, as of last year, now the maximum number of bucks one can take has been reduced from five down to three: 1 in ML season, 1 in gun season, and 1 with a bow. Honestly, with the buck/doe population as out of whack as it is, they are not going far enough on that, IMO. I think you should be allowed only TWO bucks total for the year: One with a bow, and one in EITHER ML season or gun season - your choice. Then there'd be a lot more does shot during ML season, as hunters would think twice about whether they want THAT buck, or want to hold out for a bigger one that might show itself during the rut during gun season later on. Of course, you can still get the 6 or 8 does or whatever it is, if you choose to maximize that route of hunting, and are able to find them.