[easygenes]

Yeah. Squared error is optimal when the noise is Gaussian because it estimates the conditional mean; absolute error is optimal under Laplace noise because it estimates the conditional median. If your housing data have a few eight-figure outliers, the heavy tails break the Gaussian assumption, so a full quantile regression for, say, the 90th percentile—will predict prices more robustly than plain least squares.

[c7b]

True. But it's worth mentioning that normality is only required for asymptotic inference. A lot of things that make least squares stand out, like being a conditional mean forecast, or that it's the best linear unbiased estimator, hold true regardless of the error distribution.

My impression is that many tend to overestimate the importance of normality. In practice, I'd worry more about other things. The example in the OP, eg, if it were an actual analysis, would raise concerns about omitted variables. Clearly, house prices depend on more factors than size, eg location. Non-normality here could be just an artifact of an underspecified model.