if you use a single model with 4 outputs, an output layer implicitly models covariance (ie produces correlated predictions)
but that’s a model with fully shared parameters/features in hidden layers, that may be good or bad depending on how this matches with the true process. when this is undesirable, it is possible to have model designs with some non-shared parameters and/or layers, aka multi-task learning
what you’ve described is an extreme non-sharing design, its primary downside is O(num_outputs) time&memory costs