A default looped back AXI stream, transmit (mm2s) to receive (s2mm), prevents the transmit channel from overrunning the receive channel to cause a loss of data. The tready signal of the AXI stream allows the consumer of an AXI stream to indicate it is not ready to the stream producer so that the flow of data is stopped.
A default looped back AXI stream is easy for prototyping but may not represent a real-life system accurately. A typical A to D converter produces data at a specified data rate assuming there is a consumer of the data at the specified rate otherwise data is lost.