While I agree with you that it would be a great idea to put up warning signs, I think I understand why they don't. In my youth, the towns and state forest people would put out signs saying that the ponds were not safe yet for on-ice activities.
If they do not put out signs, and only issue general warnings to make sure that the public check the ice to make sure it is safe, going on to give the thickness of the ice for varying activities, a case can be made that there is no liability for going on the ice for the town or state.
If they put out signs saying this ice is not safe, the implication is that other areas are safe and if someone goes through that ice, it becomes a case of " well, you didn't say this ice wasn't safe" .
Our litigious society at work.
Knowing where you are entering the lake, whether in a vehicle, on a snowmobile / ATV / other over snow vehicle, or on foot, you have to know for yourself how safe is the ice, and what factors in the area will affect how thick the ice is.