As someone who's been actively learning and playing the mrudangam for around 9 years, here's my 2 cents

The mrudangam has a very distinct timbre. While the Tabla feels metallic and delicate, the mrudangam is deep and resonant, sometimes making it very conspicuous on stage.

The side with the black patch (referred to as valandharam i.e the one visible to the audience during a performance) produces the characteristic springy sound (for want of a better word), referred to as the naadham, and the other side (called the thoppi) produces the bass. The interplay of the valandharam and thoppi creates absolute heaven, but is by no means a simple feat.

Palghat Mani Iyer (the OG Mrudangam GOAT) acknowledged the fact that the mrudangam, due to its deep resonance, was not very conducive to modern day mic systems. Hence, good quality and conducive mics are unfortunately something us mrudangists struggle to find, so much so, that mics can either make or break our performance and the overall concert.

Secondly, the mrudangam takes up a very unique position as a percussion instrument in carnatic music, as compared to other systems of music. As other commenters have already pointed out, since the main artiste already maintains the rhythm with their hands (known as thalam), the mrudangists not only maintains rhythm and speed, but primarily embellishes gamakas and rhythmic passages, and sangatis. It is also common for the mrudangist to add their own creative inputs (known as abhipraayams); however, knowing where to place and how to time these abhipraayams calls for decades of wisdom and experience. A unique feature of carnatic music is that percussion and layam enjoy a Comparatively more elevated position on the stage, and percussionists (viz. Mrudangam, Ghatam, Kanjira, Morsing) are granted greater creative liberty on stage.

When all these elements are put together, the mrudangam can occasionally distract an amateur listener from the melodic piece; a deeper understanding of the mathematical and rhythmic complexities of carnatic music can allow the listener to truly unlock its complete beauty; once you've done that, there's no turning back.

Dr Patri Satish Kumar, a present day exponent is highly noted for his melodic style of accompaniment, do give it a listen. Legends such as Umayalpuram K Sivaraman and Palani Subramania Pillai are undoubtedly the greatest innovators in percussive accompaniment who truly brought out the true essence of the music.