Anyone could explain me what the authors of this paper mean when they say that "The Black–Scholes model, in spite of its popularity, has some well-known deficiencies. Firstly, a closed form formula is not known for many liquid option classes such as American and Barrier options. This forces one to use computationally expensive simulation based methods to price these options, which do not scale well when the payoff of the option depends on the dynamics of multiple securities, that is when the option is high dimensional"?
I know that the results of BS can be always extended to the $n$-dimensional case.
Thanks in advance for any clarification.