Batch Normalization in the training process of ANNs makes a significant difference to convergence rates because $($choose the most appropriate$)$:

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in a somewhat deep ANN, at an intermediate weight layer if a training sample $($mini$-$batch$)$ causes significant modulation of the weights, then the outputs from this layer will need to be balanced by corresponding modulation of the succeeding weight layers down the line destabilizing convergence in the training process; this is damped by normalizing the summed inputs into the activations at each layer

to reduce possibility of destabilization in training, one uses very small values of the learning rate parameter

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the parameters of batch normalization are considered as additional parameters during training which increases the scope of optimization

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does not really help as the activation functions at a layer are in any case bounded, while batch normalization is effected on the inputs to these activation functions.