RNNs seem to take much longer to train in most if not all cases. I assume this is because the number of operations involved in training an RNN scales not only with the number of examples being fed into the network, but also with the number of timestamps. Where a regular network does one operation, an RNN does $n$, where $n$ is the number of timestamps per sequence.
For various text and time series related problems, I've switched out RNN layers (i.e. LSTM or GRU layers) with pooling layers that simply average over the temporal dimension. This leaves you with an ordinary network with Dense layers. These non-recurrent networks have always performed just as well as the RNN, but they train much faster.
Which brings me to my question. RNNs require more training time to reach the same level of performance as a non-recurrent network. So what is the point of using an RNN? In what situations are RNNs are a better choice than averaging over the time dimension and using a run-of-the-mill Dense network?