Ddha is the voiced aspirate of the retroflex class, combining the curled-back tongue position with breathy voicing, and it is among the least frequent consonants in classical Sanskrit. Its presence in the table follows from the system rather than from the vocabulary, as it does for the corresponding letter in the palatal class.
Each of the five classes is built on the same two features, voicing and aspiration, crossed against a single point of articulation, and the fourth slot is where both features are present at once. A reader who knows the rule can name the letter from its position without ever having met it in a word, which is exactly what a learner in Japan studying the table would have done.
Siddham writes the sound with a letter of its own, as the Brahmic scripts do throughout, rather than deriving it from the plain voiced stop with a mark. That is a design decision with a consequence: it keeps the fourfold structure of the class visible at a glance, and it makes the table a picture of the analysis rather than a shorthand for it.
On the page the letter takes the vowel marks and the inherent short a. Its conjuncts are few, because the vocabulary that would produce them is small.