"In randomized experiments, the effects of this variable are distributed among the groups by the randomization in a way that is taken into account in the standard tests of significance. ."
Cochran 1957. NB "distributed". He does not say "balanced."
See also https://errorstatistics.com/2020/04/20/s-senn-randomisation-is-not-about-balance-nor-about-homogeneity-but-about-randomness-guest-post/