Yes, it is useful to learn Sanskrit for many reasons:

1. It is the language of the Vedas and Upanishads, which contain some of mankind's highest and most subtle spiritual discoveries and express them in beautiful metaphors.
2. It is highly logical, complete, systematic and consistent in its alphabet sounds. It only uses the most natural sounds in its vowels and consonants. It doesn't use any vague or ambiguous sounds that change based on their position in a word, and that are "dialectized".
3. It has a very sophisticated grammar that is highly capable of describing the most intricate and subtle human thought, and the grammatical engine is capable of producing an infinite variety of verbal forms.
4. It is the language of the Ramayana and Mahabharata which are the foundation of Indian culture.
5. It is the language of great poets like Kalidasa, Bharavi, Bhasa, Bhavabhuti, Magha, Shudraka, Dandi, Kshemendra, Kaiyata, Bhallata, Bhartrihari, etc who have dug deep into mankind's psyche and mined all the treasures of poetic expression there are. The sheer volume of beautiful poetry is enough to spend one's lifetime in, if one had the means.
6. It is the language of the technical and worldly sciences such as government, economics, mathematics, astronomy, metallurgy, chemistry, botany, zoology, agriculture, medicine, architecture, civil engineering, etc. The survival of age-old temples with their intricate designs through a thousand years of violent invasions and destruction speaks volumes as an example of the accomplishment of ancient Indians in physical sciences.

Sanskrit is the heart and soul of Indian civilization.