Cell Specific Reference Signals are used in Channel Estimation. Release 8 DM-RS was a separate signal used for Demodulation Only (as far as I know). In LTE, Transmission modes 7 - 10 came rather late to the LTE specification ( Not sure whether it was 3GPP Release 10 or later) compared to Cell Specific Reference Signals and DM-RS was spatially multiplexed (i.e. transmitted on different antenna ports). This new DM-RS has a two-fold use :- You can do Channel Estimation and get DL-SNR (which can be used for CQI determination) and you can also use the DM-RS to do Demodulation ( i am not sure how).
The main advantage of DM-RS which is UE specific is the base station can transmit the reference signal when there is data to be transmitted (on the PDSCH) . I believe the CSRS has to be transmitted periodically and this would cause interference in a Multi Antenna Multi antenna scenario.
That's perhaps the main reason they did away with CSRS. Here is one link (perhaps you already found it):
https://ourtechplanet.com/5g-nr-what-makes-5g-better-than-lte/