I'm hardly going to argue about it.
Let's just say that the 'ddh' in Siddha is the same as in the word Buddha (agreed?). And we all know how that is pronounced. According to your 'system', this is pronounced 'BOO-tha'. Another famous word is 'dharma': that would become 'THAR-ma'.
Whatever.
PS.
Can you show me one Indian word (ANY language) with 'th' that is commonly changed to a 'd' in English? No, you can't. You're thinking of the opposite phenomenon, where English words with 'th' are spelled with a 'd' when transcribed into an Indian script. Which is due to the fact that Indian languages don't have the typical English 'th' (a dental fricative). That's the root of our disagreement here: you, like most Indians, mispronounce the English 'th'. You think it's like a 'd'.