It is not efficient if you are depending on it to move large volume of critical data (needed for the system processing, for example). Also looking at the example here:
https://rocketboards.org/foswiki/view/projects/datamover The H2F bridge is running at 128-bit width to the FPGA at 133.33MHz (~2.1GB/s of bandwidth) vs the DMA which is running at 64-bit width to the L3 Interconnect at L4 clock of 100MHz (~0.8GB/s).
If I am not mistaken the DMA is still useful to perform task such as moving the FPGA rbf image for programming the logic (where you boot HPS first, then program FPGA). Just probably not for bandwidth-starved applications :)