Being a fretless, bowed, string instrument, the violin is exceptionally good at the gāyaki ('as sung') style and in bringing out the ornaments, or gamaka, that are so pervasive in Indian classical music.
With the violin, there are some modifications to playing style and tuning compared to Western classical and baroque music: pizzicato is extremely rare, and col legno rarer still. The GDAE strings are tuned to x, x + 5, x', x' + 5 respectively, where x and x' are any note and that note an octave higher. Typically x = D♯, E, or F in violin solos, and x = the vocalist's/main artiste's choice of śruti when accompanying.
It is for precisely this reason that the harmonium and similar keyed instruments like the piano are eschewed in Indian classical music (barring a handful of exceptions). With so much focus on melody and ornamentation instead of harmony, multiple simultaneous keypresses are incongruous in Indian classical music, and the piano is unable to do any trill, glissando, or equivalent gamaka that the violin, flute, or even the mandolin can. Electronic keyboards are somewhat less frowned upon, because the synthesiser can approximate gamakas.
That said, even today, many conservative listeners will not accept anything but the violin, which has been part of Carnatic music for more than two centuries.
[1]: https://maddy06.blogspot.com/2018/10/the-violin-in-carnatic-...
An addendum: My comment has a slight Carnatic bias. The harmonium still exists in Indian classical music today, but it is significantly more popular in Hindustani music than in Carnatic music.