For a regression model, can you transform all your features to linear to make a better prediction?
Your idea is good, but you are not the first with this idea.

You can use Generalized Additive Models (GAM) with regression splines to check and/or add non-linearity in a linear regression setup. There is a clear advantage over looking at just descriptive figures one-by-one (with manual feature generation), since you can estimate a whole model with extreme flexibility.

Alternatively, you can simply do a linear regression with a lasso penalty. Add polynomials to your $X$, and let the lasso „shrink“ irrelevant features to zero.

The book „Introduction to Statistical Learning“ covers these topics in Sections 6,7.

BTW: even with polynomials, your model can retain interpretability if you care for this. Polys are relatively easy to interpret. However, under a GAM approach, interpretation is a little more difficult.

Maybe as a note: you want to make features linear (which can be a problem since you can only apply linear transformations to the data). The approaches proposed above aim at making your (linear) model more flexible to cope with non-linearity in data.