Even supporting a database of millions of songs would be possible.
Every year gives us around 100 popular songs (add a % of location-specific popular ones), so it seems the plan is feasible.
Even if it takes up a small amount of space, it's basically a non-feature.
Many of those songs have never been played[1]. There's a really (really, really, really) long tail.
[1]: http://forgotify.com/
https://blog.afterthedeadline.com/2010/01/29/how-i-trie-to-m...
Even supporting a database of millions of songs would be possible.