[1] Random assignment of participants helps to ensure that any differences between and within the groups are not systematic at the outset of the experiment.
[1] Thus, any differences between groups recorded at the end of the experiment can be more confidently attributed to the experimental procedures or treatment.
[1] Random assignment, blinding, and controlling are key aspects of the design of experiments because they help ensure that the results are not spurious or deceptive via confounding.
Studies done with pseudo- or quasirandomization are usually given nearly the same weight as those with true randomization but are viewed with a bit more caution.
This is a rare event under random assignment, but it could happen, and when it does it might add some doubt to the causal agent in the experimental hypothesis.
[2] Because most basic statistical tests require the hypothesis of an independent randomly sampled population, random assignment is the desired assignment method because it provides control for all attributes of the members of the samples—in contrast to matching on only one or more variables—and provides the mathematical basis for estimating the likelihood of group equivalence for characteristics one is interested in, both for pretreatment checks on equivalence and the evaluation of post treatment results using inferential statistics.
Charles S. Peirce randomly assigned volunteers to a blinded, repeated-measures design to evaluate their ability to discriminate weights.