The only advantage was that you could record in them. Then recordable CDs arrived and BOSH.
They still had a good following from (mainly amateur) DJs for quite a while after recordable CDs arrived. It was really easy to connect up a minidisc recorder and record sets – not so easy with CD!
Also, even when you could sit at home and burn CDs, playing them on a CD player while on the move was rubbish compared to a MD.
However it wasn’t too long before flash type media (data sticks etc) took off and they were the most practical of all, killing off the MD completely.