In experiment, if you know before that an attribute $X$ may affect the treatment effect, so you could do stratify sampling from your target population, e.g., if $X$ is weight, then you could divide the target population into several buckets, then do stratify sampling first, then within the sample from each bucket, you run a completely randomized experiment. Note that the stratified sampling method completely eliminate the small chance that some minority bucket gets very low number of samples.
Now, if you didn't do stratify sampling, instead, you just did random sampling from your target population, then I think there is no point to do blocking in your sample, i.e., first split your sample into several cohorts based on the value of $X$, then within each cohort, do completely randomized experiment. I think there is no point of doing that. Because one could just run completely randomized design on your entire sample and then in the post data analysis, you just run a linear regression incorporating $X$.
So my question is: if you don't have stratify sampling first, then blocking is useless, I am not sure if this claim is correct.