When should I NOT scale features Feature scaling can be crucially necessary when using distance-, variance- or gradient-based methods (KNN, PCA, neural networks...), because depending on the case, it can improve the quality of results or the computational effort.

In some cases (tree-based models in particular), scaling has no impact on the performance.

There are many discussions out there about when one should scale their features, and why they should do it. Apart from interpretability (which is not a problem as long as the scaling can be reverted), I'm wondering about the opposite: are there cases when scaling is a bad idea, i.e. can have a negative impact on model quality? or less importantly, on computation time?
Scaling often assumes you know the min/max or mean/standard deviation, so directly scaling features where these information is not really known, can be a bad idea.

For example, clipped signals may hide this info, so scaling them can have a negative result because you may distort its true values.

Below is an image of 1) a signal that can be scaled, and 2) a clipped signal that scaling should not be done.