I am not sure what large means in this context, but I believe if the idea of randomization is achieved with "enough" subjects in a given experiment.
Fisher developed the theory of randomized controlled trials for their particular value for causal discovery. He described a randomization as an intervention that assigns treatment at random after all disturbing causes are determined (in the sense of “set”, not in the sense of “discovered”).
Ideally, treatments should be “the last in time of the stages in the physical history of the objects which might affect their experimental reaction.”
Interventions are used to create circumstances that support the inference from a particular observed association between the treatment and the outcome to the causal influence of the treatment on the outcome. The randomization is supposed to ensure that no influences other than the intervention determine the state of the intervened variable and that consequently any confounding due to known or unknown common causes can be eliminated. This feature is a guiding consideration in specifying interventions as discovery tools.