When would one use a hard margin SVM? Is there ever a good case to use a hard margin SVM? It seems far more likely to overfit and doesn't seem computationally faster than a soft margin SVM, so there doesn't seem to be any reason to ever use it.
 A: This is analogous to "why use linear regression if ridge regression is available" - if your primary goal is predictive accuracy, you wouldn't.
Since SVMs are only used for predictive modeling, I don't think there is much real world use for hard margin.  The soft margin problem includes the hard margin as a special case, so if you're doing everything properly, your hyperparameter tuning of the soft margin will find the hard margin solution if that maximizes the predictive power of the model.
That said, hard margin SVMs are useful to understand as a stepping stone to the soft margin case.  So there is pedagogical and mental mapping use for them.
A: The real world problems aren't linearly separable usually, thus you can't use hard margin. However if you find a mapping corresponding to a kernel that make transformed data linearly separable in the Hilbert space you can use hard margin. This is equal to extract features from training set according to mentioned mapping and using feature data as new training set. If the mapping make feature data linearly separable you can use hard margin
