Why not use mean_pred_stderr this method to calculate standard error when estimate the whole confidence interval？

When using BootstrapInference to estimate the whole confidence interval,
The standard error of the current version is to calculate the variance of each sample according to the ITE value of the BootstrapModel, then calculate the mean value of all samples, and then open the root sign.
Why not calculate ATE for all samples first for each BootstrapModel, and then calculate standard deviation for ATE of all BootstrapModels,
I think the latter method is more suitable for the case of small data volume and high dimension, and it is also implemented in causalml.
I think the attribute mean_pred_stderr is reported in the code,you can define mean_pred_stderr mehtod in the class EmpiricalInferenceResults, as follows:
@property
def mean_pred_stderr(self):
return np.std(np.mean(self.pred_dist, axis=1), axis=0)

Start by locating the BootstrapInference and EmpiricalInferenceResults implementations, then inspect how pred_dist and the current standard error are used for whole confidence intervals. Compare the proposed mean_pred_stderr calculation with the existing behavior and determine the validation needed for small, high-dimensional data; the issue does not name a test file.