In a RCT, what are the risk of selection bias if no allocation bias is present? In the Wikipedia page about Randomized Controlled Trials (RCT), the procedures section states that RCT minimize selection bias and allocation bias.
My understanding is that selection bias "occur if investigators can consciously or unconsciously preferentially enroll patients between treatment arms" while allocation bias "occur when covariates that affect the outcome are not equally distributed between treatment groups".
Suppose we design an RCT that has selection bias but no allocation bias.
For instance, we want to test whether a new drug for the flu is effective.
We take 100 persons, and the researcher assigns the 50 prettiest (from a physical point of view) to the treatment group (receive the drug) and the 50 ugliest to the control group (receive placebo).
The outcome is time needed to heal from the flu.
There is selection bias as the allocation is not random.
However, there is no allocation bias as physical appearance does not confound the relationship. In fact, the flu does not heal faster in prettier persons than in uglier ones (or at least, suppose that is not the case. That is, let's make no reasoning like "the prettiest ones are also the youngest and the youngest heal faster"). Let's assume that the selection variable (physical appearance) is orthogonal to the outcome.
So, what are the dangers of such a design?

If you merely assume away the problem, then obviously that is going to make it difficult to see the dangers of that kind of design.
Unfortunately, reality does not let us assume away statistical relationships between human characteristics.  Prettier adults are in fact generally younger, healthier, thinner, more active, wealthier and more educated (the last two relative to their age cohort), etc., than uglier adults.  All of those are potential covariates that would be unequally distributed between the prettier and uglier cohort, so it is a textbook case of allocation bias.
Now, perhaps the allocation bias doesn't matter.  Perhaps recovery from the flu is not related to any of these things.  Nevertheless, it is not something that is a safe assumption a priori, and that is precisely the danger with a selection mechanism that chooses one human characteristic as a proxy for "randomisation" --- it is generally going to be statistically related to a whole bunch of other human characteristics that may have a causal effect on the outcome.
