I am not into the field of super resolution-resolution, but I think this question applies to general neural network construction.
Usually, you try to solve a classification problem or a regression problem with your neural network.
For classification, you try to predict probabilities that a specific output corrensponds output corresponds to a specific class. Therefore, every output value should should be a probability and therefore have a range between 0 and 1. To To achieve this, you usually use a softmax or sigmoid function as your last last layer to squash the output between 0 and 1. In addition to this (which is wanted in classification tasks), these functions raise the probability output of likely classes while decreasing the probability of all other unlikely classes (therefore enforcing the network to choose for one specific class over the others).
For the regression task, you are not looking for probability values as your your output values but instead for real valued-valued numbers. In such a case, no activation activation function is wanted, since you want to be able to approximate approximate any possible real value and not probabilities.
So, in the case of super resolution-resolution, I think the generated output is a map where each value corresponds to a pixel value of the super resolution-resolution image. In that case, your pixels are real number values and no probabilities. So, you are solving a regression problem.
But you could also go with a classification approach, where you have 256 output maps that give probabilitiyprobability to each possible pixel value between 0.$0$ and $255$.255