That is true if you assume you are starting with an unbiased coin/event etc. If you know there will likely be a bias in the outcome then its a safe bet you don't need more events.
I’m assuming a process with multiple interacting and sometimes poorly understood inputs.
Nothing so simple as a coin toss, nor quite as complex as real life.
A control chart is better suited to an engineering reality than a mathematical or political construct. Perhaps not the best tool for this particular application, but still useful.