Is there usually any long or short predominant bias on pure volatility, delta hedged books? In my mind, it would make sense to try to equalize long and short vegas to have as neutral a position as possible to cater for big crashes. Plus, if you have a view on overall market volatility you're better off trading it against the index instead of going for single names.
I don't fully understand your statement. What exposure do you recommend leaning on to make a profit? As for overall market volatility, I think you have a better edge positive gamma (long volatility) on single names and negative gamma (short volatility) on the index. Just by market movement potential and imho. Further talk of dispersion trading is out of my depth.