Religion probably played the most important role in determining the structure and construction of Indian scripts.
Earlier, in the Indian culture, writing was considered as inferior to speech. And it was important to record the Vedas too. And with speech, perhaps, the content of Vedas were getting diluted.
Since Vedas had to be pronounced correctly, Brahmi, the phonetic script was born. If you see, the Arabic and Graeko-Roman forms are derived from pictograms or ideograms. The Indian letterforms are schematic designs based on the classification of the vedic sounds.
Later, the archaic, cursive forms of Maheshwari Brahmi evolved into the angular forms of Ashokan letters and further into Bharati, Devalipi (Nagari) and Devanagari.