How to understand regularised linear models I'm working on a project using elastic nets for predicting a continuous variable using multiple attributes. I'm struggling to understand some of the underlying theory behind what I'm doing.
I understand that higher gradients are penalised more than shallower gradients, but why? What if a steep gradient does genuinely fit the data well and cross validation supports this?
I can access the gradients in python using the .coef_ attribute. How can you interpret these straight line gradients if you have attributes with different scales, and you have scaled the data before training?

The term gradient is misleading and makes the question vague. The term coefficient is more suitable. So, I'll write my answer accordingly.

I understand that higher gradients are penalised more than shallower
gradients, but why? What if a steep gradient does genuinely fit the
data well and cross validation supports this?

It's regularization. Especially, after the features are standardized (target regularization also helps), the likelihood of large weights fitting the data diminishes. And, the regularization makes sure that unlikely fits will not occur. You could always form an unregularized model and compare it with the regularized models during your model selection (using a validation set, or cross validation). If the unregularized model wins over the others, you can choose to use it. Regularization is a way to fight overfitting. If your unregularized model is able to generalize well, then there is no problem.

How can you interpret these straight line gradients if you have
attributes with different scales, and you have scaled the data before
training?

The coefficients found for scaled features/attributes can be converted back and interpreted in the original scale. If the coefficient found is $w$ and the original feature was $x$, we'd have the coefficient scaled back to original feature dimension as (considering standardization for example)
$$w(x-\mu)/\sigma=\overbrace{\frac{w}{\sigma}}^{w_{orig}}x\overbrace{-\frac{w}{\sigma}\mu}^{\text{Joins the intercept}}$$
Since $w_{orig}$ is multiplied with $x$, the feature in its original scale, it can be interpreted that way.
