It's not that simple because that way you lose too much information. Actually it is more likely the whole system would fail if weights at any layer are reset.
The idea was developed mostly for transfer learning as in learn new stuff on a new domain but do not forget the old stuff as well. For forgetting it could be trained on some old images + all zeros target mask and the MAS to preserve everything else.
There is a way to selectively unlearn something via Memory Aware Synapses (MAS): - https://arxiv.org/abs/1711.09601
The idea was developed mostly for transfer learning as in learn new stuff on a new domain but do not forget the old stuff as well. For forgetting it could be trained on some old images + all zeros target mask and the MAS to preserve everything else.