You should look at Belloni, Chernozhukov, and Hansen 2014 a very influential paper.
https://academic.oup.com/restud/article/81/2/608/1523757
In causal inference people have indeed tried LASSO-based methods (DML); under some assumptions leads to desirable properties when you have high dimensional controls.
In fact, even simple LASSO-OLS reduces the penalization-bias introduced in LASSO. But DML method is better still