There is no valid reason for keeping the two airlines as separate entities, given their obvious synergies. Both airlines fly from Chennai to Singapore on the same day, within hours of each other, and both maintain expensive offices in Singapore.
On other routes like those in the Gulf region, they even undercut each other; according to a presentation Air India once made to the civil aviation ministry, its yields on Gulf and South east Asian routes were the highest for destinations where Indian Airlines did not fly! The synergies flowing from marrying the two airlines