When we speak of the benefits of randomization, we talk about the balance of covariates so as to mitigate the possible confounding due to selection of treatment. That is, if a design were replicated again and again, each patient would be equally likely to be assigned to treatment or control. Why then do we not assign treatment in a systematic 1-0-1-0-1-... fashion? If we view the order of a participant's entry into the study as random so that their order of entry is equally likely to be even- or odd-numbered, would that effectively solve the same type(s) of biases as unconditional randomization?
If the randomization sequence is discovered, patients could be non randomly assigned to the experimental group of choice. In a truly blinded study, this is unlikely. In many studies, blinding may not be possible, which would expose a simple 1-0-1-0- process. Many investigators attempt to provide care through RCTs and hope for treatment group assignment when, theoretically, equipoise allows conduct of randomized assignment.