Targeted Maximum Likelihood for ATE, why not just GLM for ATE? I have been attempting to learn targeted maximum likelihood (TMLE), which is a struggle. The estimand of interest is often the average treatment effect. If we have an outcome $Y$, intervention $A$ and a set of covariates $W$ this is defined as,
$$ATE = $$
$$E_W( E(Y|A = 1, W) - E(Y | A = 0, W)) = $$
$$ E_W( E(Y|A = 1 ,W)) - E_W( E(Y|A = 0,W))$$
where $E_W$ denotes the expectation with respect to the distribution of the covariates. Why do we need targeted maximum likelihood here? For any GLM I can estimate $E_W( E(Y|A = 1,W))$ by first just finding $E(Y|A = 1,W)$ explicitly from the GLM (similarly for $E(Y|A = 0,W)$)  and marginalizing out over the distribution of my covariates. What is TMLE getting me here that traditional MLE of a GLM is not?

If the dimension of $W$ is large, computing the MLE of the whole GLM and then marginalising need not give the efficient estimator of the ATE.  From an asymptotic viewpoint, suppose the dimension of $W$ grows fast enough that the whole parameter vector of the GLM is not estimable at $\sqrt{n}$ rate. It's still possible that the ATE is estimable at $\sqrt{n}$ rate, and that the plug-in estimator you describe isn't efficient.
Heuristically, efficient estimation of the GLM (by maximum likelihood or any other way) involves getting the bias:variance tradeoff right for the whole parameter vector. But for causal inference what you care about is a particular one-dimensional functional of the parameter vector. It turns out that the optimal tradeoffs can be different. Targeted MLE focuses on estimating the one-dimensional parameter of interest, and accounts for the need to estimate the other parameters by considering the one-dimensional submodel of the GLM in which estimation of the ATE is hardest.
If the dimension of $W$ is small enough that the whole GLM can be estimated well, the simple plug-in estimator will be efficient.  This is what you get with an asymptotic argumen that treats the dimension of $W$ as fixed as the sample size increases.
See also this answer
