That's an interesting need gap, considering I have access to both music in India which has a song for every instance of life in dozens of languages and from western countries; categorising songs based on lyric would be an achievable task. In-fact this had been attempted in Deep Learning research - https://www.aclweb.org/anthology/C14-1059 in limited capacity.
I haven't seen a commercial music app which can categorise by lyric and even then finding songs for certain categories like Science, Pets are going to be hard. Perhaps youtube songs like Geek vs Nerd and their likes could be featured.
The reason why music industry favours love, sexual songs is because it sells, listeners can relate to it and most famous songs are written by the same lyricists. I would love songs categorised by lyrics, say 'The Hamilton Mixtape' under History would be great. I could remember many great songs to be categorised under Philosophy in Indian languages as well.
I hope that there are others who share similar views on this need gap.