I've found that a lot of people are skeptical towards system dynamics as a method. I also have a hard time explaining what it is, especially in comparison with other modeling methods such as conventional economic modeling because I don't really know much about other modeling methods.
One common criticism is that it is too subjective because system dynamics models can accommodate subjective variables such as level of material well-being or crowding. While system dynamics can be used to model completely physical systems where we already have a pretty good understanding of the dynamics, such as a pendulum, it is more often used for modeling social systems such as the organization of a business or the urban population.
It seems that many other systems models for engineering and economics are geared towards having inputs and getting outputs. For example, how many kW should each generator on the grid be supplying, how much profit does the company expect this quarter, what percent of the profit should be spent on R&D, etc. The power of system dynamics, in contrast, is not in the accuracy of getting numerical answers, but rather in gaining understanding of the dynamics of a complicated system. A system dynamics model can help users find out the causality of different outcomes, what actions have the most leverage, and what behaviors are just symptoms. I still feel there is a lot of potential for system dynamics, but I am trying to maintain a critical attitude to better understand its limits and differences from conventional models.