Learning to play a music instrument has multiple advantages for singers of Hindustani classical music. But at the same time one doesn’t necessarily has to learn an instrument in order to learn vocal skills.
Generally speaking, students who learn vocal/singing skills, do not really need a deep understanding of music theory and usually as vocalist (except in some genres of music) students can work their way up without learning it. On the contrary, as a musician, one needs to have a strong understanding of music theory including reading and writing skills of musical notations. Learning music theory has the advantage that it improves listening skills and tunes up the ears too.
Learning to play an instrument helps to learn a melody and musical notes visually. One can play and sing along, say a difficult part of melody, on a piano and remember the notes or “Suras” as visual representation. This helps specifically students who have a strong visual memory.
Versatility with Confidence
As a vocalists, at times, to gain confidence and to get rid of stage fear, performing in front of a small group, for example a house party or at a small house concert can radically boost one’s self -confidence. But often times as a vocalist, it is difficult to keep the audience interested during a performance. Learning an instrument will enable multiple opportunities to perform in front of small groups which ultimately brings more confidence and clear understanding of one’s own capabilities.
Collaboration with Musicians
One strong advantage of learning to play an instrument is that sooner or later as vocalist, one wants or happens to sing as part of a band where s/he needs to collaborate with multiple different musicians.
From my personal experience, it bring a huge advantage when as a vocalist one understands the language of music and can talk and discuss about the notes and beats while practicing a song with other musicians. Often times groups tend to have multiple vocalists where each member has to support other vocalist in their performance and in this case, it becomes very helpful if a vocalist can take up more roles in a band.
Finally, in my opinion, it is always good to explore multiple dimensions of one’s skills even though the main interest remains in vocal skills.
Also, when life gives you only one chance, learning an instrument is worth it.
All the best.