The reason you split your dataset to Training and Test is to simulate real-world cases. What you actually do with the train-split validation is to evaluate your model in unknown data.
Imagine now that you have trained your model and you are on a production where new data keep coming for prediction. You might not get them in mass, but one by one such as in an API call. You don't have the mean and standard deviation of those "new" data. You only have the mean and std during the training process.
To sum up, train-test validation tries to be as close as possible to the real problem. And since you won't know anything about your upcoming data, you should not use any knowledge you get from the test data.