The three-way sibilant distinction is one of the features that makes Sanskrit valuable as evidence about the history of its language family, and one of the features a script for it cannot do without. A palatal, a retroflex and a dental sibilant are three separate letters, three separate sounds and, in the grammar, three separate behaviours: the dental converts to the retroflex under stated conditions, the palatal does not, and clusters behave differently according to which is present.
Most of the related languages outside India merged them. Greek, Latin and the Germanic languages have one sibilant letter and no framework connecting it to anything, so a scholar working from those alone could not reconstruct what the Indian evidence shows. The Sanskrit table sets the three out explicitly, classified by point of articulation like everything else in it, and that classification is what makes the comparison possible.
Latin transliteration handles them badly. The palatal is usually written with an acute accent, the retroflex with a dot beneath, the dental as plain s, and dropping the diacritics collapses all three. Words that differ in the language become identical, and the grammar that depends on the difference becomes invisible. The letter pages of this atlas keep the distinction where the plain spellings used elsewhere cannot.