>It is practically impossible to conduct a long term health study on something like an artificial sweetener. The only way I can think of to accurately remove environmental noise is to collect extensive records on a _large_ population, and then line up A / B sets where the only major difference between the sets (other exposures similar) are the sweeteners.
The concern with cohort studies isn't "noise", it's confounders. eg. people who eat smoked meats tend to eat other unhealthy foods, so they live shorter lives, but smoked foods in and of themselves aren't harmful. Having a bigger sample size does nothing to combat this. You can "control" for confounders, but comes with its own problems. Control for too little variables, and you still get confounding, control for too much, and you run into p-hacking territory.