Great question, Philip. Conceptually, the only thing that the process of linearization does is to 'explain out' a portion of the variance in your data.

Suppose what remains after applying a linearization function such as ln() or sqrt(), the 'residue', is largely linear. After you fit a linear model to this residual data, you will likely get a high goodness-of-fit.

But if the residue after linearization is non-linear then either the wrong kind of linearization function was used, or some more linearization is needed using one or more additional linearization functions, or as you have correctly said, its practically not possible to fully linearize the data set. In all these cases, if you try to fit a linear model to this residual data set, you will get a poor goodness of fit.

I hope that answers your question

'best