Hi,
Normalization is some kind of transformation, let’s say your data contains weights of humen then if you train your model with normalized data, model learns to predict for instance using input in range of [-1, 1] and it also predict in a range similar to that.  Then if you test your model using original values for instance [1, 200]`, your model has no idea about these huge variance and bias so it cannot  predict in the structure it was trained for.
Test/validation is a step to ensure your model had a reliable train stage, so everything need be consistent between train and test/validation, if not, how can one make sure model is working fine?
Bests