IMO, whatever other reasons there may be, a most compelling reason for learning a language is its poetry (Robert Frost defined poetry as that which gets lost in translation), and here Sanskrit poetry is unlike anything in the world. You may like to read this collection of essays[2] that my friend wrote during his first real encounter with Sanskrit poetry.
[1]: https://youtu.be/ZoS1nA8RVko?t=740 (starts at 12:20), https://youtu.be/WwtIJ8_bQf8 (ends at 35:00).