Heterogeneous Treatment Effects - should it mention the linear regression is expected to have "good" controls only?

[afurmanov]

There is an issue on chapter 18 - Heterogeneous Treatment Effects and Personalization, in the following paragraph
Predicting Sensitivity

Here is an idea. What if we use linear regression?
Let's say you fit the following linear model to your data.

$y_i = \beta_0 + \beta_1 t_i + \beta_2 X_i + e_i$

Should not it be mentioned here or maybe in some other place in this chapter that features $X$ are expected to be good controls, as defined in Good Controls section of the book, since sensitivity defined as $\frac{\delta y_i}{\delta t_i} = \beta_1$ would have casual meaning when linear regression is capable to find ATE, i.e. it is constructed according to the casual model? Or if generally speaking $X$ is just a set of observable variables, there is no guarantee the linear regression will find an ATE, and $\beta_1$ is just some regression coefficient, which would not answer the question of what effect in $y$ we see had we changed $t$ by $\epsilon$.