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?

Here's a simple example of how this experiment can go awry. Suppose you assign people to treatment based on beauty, which has no direct effect on recovery time. But beauty can help attract a partner that brings the patient chicken soup, thereby aiding the recovery. A second channel is that a partner will nag the patient to take the medication, which is a kind of increase in treatment intensity/dosage. This will make it hard to estimate the direct effect of the treatment since the treated group will have more partnered people relative to the control group.
