You have presented many interesting points with respect to vector-loop modeling and Monte Carlo simulation, although it is not really valid to make a comparison of these two technologies. Vector-loop modeling is a constraint system definition, not a solver technology. The public information available on this subject is a little confusing and limited. Most of this information doesn't precisely discuss defining the assembly functions and part feature relationships through different modeling methods vs. how the functions are initially solved, and then how the solved solution is finally analyzed/reported. There are generally two tolerance solver technologies used in current commercial applications: Monte Carlo Simulation and derivative-based analysis, both of which are supported in CETOL. A vector-loop model can be solved with either of these solution approaches.
In your post, you mentioned the fact that Monte Carlo simulation supports the ability to account for variations that occur due to manufacturing methods and machines. Actually, that capability is supported by both of the solution approaches (Monte Carlo and derivative-based analysis). In fact, that is much more conveniently accomplished in the derivative-based analysis approach because the manufacturing variation can be incorporated into the analysis as a post-processing function. Once the derivatives (sensitivities) have been calculated, the results can be recalculated quickly (almost instantaneously for most models) when manufacturing variation data (or any other input data, for that matter) is entered. With a Monte Carlo approach the entire simulation of the original model with the new manufacturing variation information must be rerun, as it would with any change in input data. This is one of the inherent problems with Monte Carlo simulation.
There are conditions where one solver may be more beneficial than another. Both are capable of generating results for large, complex problems However, with Monte Carlo solvers it is difficult, if not impossible, to ascertain the validity of the model that is being solved or, more importantly, the accuracy of the results. A derivative-based analysis provides the derivatives (true sensitivities) and contributions that show the precise mathematical relationships between the measurements and dimensions. Thus, the sensitivities and contributions can be used to verify the validity of the model and accuracy of the results. This is the most significant differentiation in the overall benefits of one solver method vs. the other: the ability to use the output to clearly understand the model, eliminate the error associated with modeling assumptions, and provide higher confidence in the results' ability to predict and correlate with the real manufactured product.
Many of commercial applications that use the Monte Carlo solution approach provide tools for estimating the sensitivities and contributions. However, these calculations are incompatible with many of the models created in those applications because of the discontinuities and nonlinearities inherent in the modeling approach used. Thus the sensitivities and contributions that are reported in those applications can be highly misleading.