I think his point is that Black-Scholes et al are holed beneath the waterline precisely because they involve standard deviations. In his world, you're better off being unable to price an option than you would be with Black-Scholes. Your example of "That put option is currently selling at 30% vol" is actually an example of why the system is so completely broken: if volatility as standard deviation was valid, all options against the same underlying instrument would have the same implied volatility. The volatility smile shouldn't exist.
This wouldn't matter if the down-side wasn't so crippling.
I don't think Taleb has to be the one to propose a replacement for portfolio theory, and I think criticism of him for not doing so is pointless. You don't need to have a spare tire handy to point out that your neighbour's car has a flat, and you don't have to run an airline to tell people not to get on a plane with the engines visibly on fire.
I've never understood this part of Taleb's argument. Of course, constant vol Black-Scholes does not hold. BUT NO ONE USES THIS. Everyone in the financial industry is well aware of the volatility skew, and spends lots of time adjusting for it.
B-S vols are putting the "wrong number into the wrong equation to get the right price" as Rebonnato famously said.
This wouldn't matter if the down-side wasn't so crippling.
I don't think Taleb has to be the one to propose a replacement for portfolio theory, and I think criticism of him for not doing so is pointless. You don't need to have a spare tire handy to point out that your neighbour's car has a flat, and you don't have to run an airline to tell people not to get on a plane with the engines visibly on fire.