Is a test set necessary after cross validation on training set?
In &quot;The Elements of Statistical Learning&quot; by Hastie et al the authors describe two tasks regarding model performance measurement:

Model selection: estimating the performance of different models in order to choose the best one.
Model assessment: having chosen a final model, estimating its prediction error (generalization error) on new data.

Validation with CV (or a seperate validation set) is used for model selection and a test set is usually used for model assessment. If you did not do model assessment seperately you would most likely overestimate the performance of your model on unseen data.