Lets take a simplified case were the population small so its practical to compute the exact sampling distribution.
Population size 3 people (A,B,C)
Suppose your sample size will be 2.
There are 3 possible samples: AB,AC,BC.
Lets say we followed your method and randomly sampled (AB), but did not return them to the population. What will happen next? there is only 1 person left for you to sample from but you cant include A or B in any future sample; so your calculation will ignore any results associated with AC and BC.