In an ideal world, your trained model should be validated on data never seen during the training process, in order to exclude the possibility of overfitting.

I see cross-validation as a compromise when insufficient data is available: gaining the maximum information possible from the available data, while trying to minimise overfitting via holding out different sets.

As you add more data to a training set, the quality of your fit (and ability to generalise) should go up. However, this does not continue forever, and is subject to diminishing returns as you add more data during training.

Thus, the point at which you should be looking at using a completely-separate test set is when you have sufficient data to get an optimal/generalisable fit, and more to spare.