hypeparameters tuning neural network according to loss vs according to scoring function
If you look for example at the L2 loss function:

$$
\sum (y - \hat{y})²
$$

It takes into account how much the predicated value differs from the actual value. Note that because of the squaring of errors, L2 is sensitive to outliers. So, as you can see it takes into account how far our predictions are.

And that is exactly the problem: Most of the time we are not interested in how far our predictions are from the ground truth. 

Imagine a real world application where the model predicts an image label. The application won't give you n examples together with their probabilities. It will just output the image with the highest probability.

That means, in the case of a classification problem where we use a softmax together with cross-entropy-loss it is not important if the predicted probability for a class is 0.49 or 0.01. We only care about if our model got the class correct or wrong.

Also, accuracy is much more tangible and better to interpret. That's why accuracy is used much more often.