Yeah, reading through the Wikipedia, it looks like this reduces the total error of the combined estimator, but the error compared to an estimator of any one sin

Yeah, reading through the Wikipedia, it looks like this reduces the total error of the combined estimator, but the error compared to an estimator of any one single parameter could be worse. So you can combine whatever crazy parameters you want, but it's only really relevant when you have things that are associated with each other somehow, and you want to reduce the total error of estimating all of them.