you can listen to a CD more than once in quick succession without permanently distorting it

you can play a particular track on demand

you can reproduce a disc without quality loss

rewinding a DVD is pretty quick

DVDs include subtitles; tapes didn't

CDs and DVDs are significantly smaller and easier to store than records and VHS tapes - I have a pocket-sized container that will safely hold a couple dozen CDs, but that would be fairly difficult with records.

In summary, CDs and DVDs are both vast technological improvements over vinyl and tape. And I have no idea what you're talking about with "And they were far more fragile."