A really interesting example of this is the MTV animated series Daria (1997-2002). The show would play licensed music and the pop/alternative hits of the day, making it feel very 'of its time' -- this was when MTV was at the height of its cultural relevance.

Then years after the show went off the air, they released DVD versions that stripped out every single song and replaced it with random royalty-free music. It really hurt the episodes.