There are several reasons why you should learn Sanskrit. Some serious and some not so much. But I would say you should learns Sanskrit because it is so much fun!
Apart from the fun, learning Sanskrit can also help you understand the etymology of a lot of words in Indian and non-Indian languages. It would also help you understand ancient Sanskrit texts, shlokas and other Sanskrit words in their true context, with nothing getting lost in translation.
Sanskrit is also a very systematic and syntactic language and the grammar of the language servers as a master template for most Indian (and a few European) languages.