You really don't know how the military works.
To train one nuclear power qualified person in the Navy it costs more than a million dollars. Just for one. When a Navy nuke gets out of school, they have enough knowledge and training in their background to get a pretty good job at pretty much any power plant, nuke or conventional, in the country plus other places dealing with construction, maintenance, and QA of power plants. Such an idea would absolutely cripple the Navy's fleet, since many nukes would just join for the free training, get out, and get a job with much better benefits and pay than the Navy. There would not be enough nukes left in the Navy to actually run the engine rooms of either the subs or the aircraft careers, all of which are nuclear powered.
And this is just an example from one job in one branch of service. As an overall policy throughout the military, we would not have a lot of personnel left, especially not in the highly technical and/or highly undermanned jobs. It just wouldn't work.
Besides, if someone absolutely wants out of the service now, they can do something that would get them a general or OTH discharge. Yeah, it would suck, but it's not like they wouldn't be able to live with it.