If the distribution of the residuals are not normal, then you might want to consider other methods since the predictions and confidence intervals are likely to be misleading. Ease-of-computation doesn't seem like a good enough reason.

In terms of clock cycles, it's more expensive to create models than it is to make predictions from them. I would imagine that you'd create the model(s) relatively infrequently (but use them a lot), and so the model creation speed might be decoupled from your process.