If the holidays are justified, so are the special sessions.
The best would be 365 days per year, leaving it to the traders to take apprpriate weekly off based on their own suitability, or work on all days.
With online trading and internet networking, gone are the days of the need of 'Trading Ring' where physical presence was required. Now, one can work from home too. Internet banking could solve the settlement problem, by crediting/debiting through RTGS.
NSE is a baccha,but on BSE, it had been taking place over a century, So, what's the problem?