Yes, the way the ensemble model calculates the probability is as you explain : for instance for the rain, each dot of the 21 dots can give a different level of rain (1mm, 4mm, 10mm,...). Based on that set of different levels of rain, the model can calculate several probabilistic values such as the average, variance,... This will allow you to quantify the risk of rain
Now, if the model has to adopt the same approach for many other parameters, such as pressure, temperature,... And for each parameter do the 21 calculations (do not forget that each calculation is the equivalent of a single deterministic calculation), computional limitation will be the issue if the model keeps the same grid. To overcome this problem, grid is bigger, calculation of the 21 dots for the different parameters becomes ok but accuracy will decrease.
Computational calculation is key. In average, weather forecast improves by one day every 10 years thanks to the computer (super calculator) progress