First of all, according to D. Tan, that 'antibiotics never completely eradicate a bacterial population' is correct.
Here are some proof-
Any bacterial species has a characteristic level of susceptibility to any given antimicrobial, which has been dubbed “intrinsic resistance."This means that, for any given concentration of antibiotic, a part of the population present in the microbiota (the most susceptible one) will be inhibited and another part will consequently increase their abundance.
Bacteria present a core genome that is shared by all members of the species and an accessory genome that is specific to each member of the species. The first encodes the most basic processes of the organism, and the second encodes the most adaptive ones: for instance, those that make the commensal bacteria Escherichia coli become a dangerous pathogen, those dealing with antibiotic resistance, or several involved in the biodegradation of toxic compounds.
If an antibiotic doesn’t kill all the bacteria that infects a patient, the surviving bugs may be particularly adept at timing their resurgence.
Theoretical scientists at Rice University have proposed a better way to understand how to prescribe antibiotics to kill every last bacterium or at least discourage them from developing resistance.
Antibiotics are used in acne for both the eradication of P. acnes and for their anti-inflammatory properties. The antibiotics used in the management of acne include both topical and systemic forms.
Propionibacterium acnes (P. acnes), the microbe that resides and can be abundant in the pilosebaceous unit, is associated with the severity of acne. P. acnes is an anaerobic organism that is part of the normal skin flora . Obstruction of the follicular opening of the pilosebaceous unit provides an ideal environment for these bacteria to grow.
Note that Propionibacterium acnes (P. acnes) = Cutibacterium acnes (C.acnes).
Now coming back to the question,
By giving the antibiotic therapy the main bacterial population which causes the clinical symptoms is eliminated.
Talking about the remaining commensal bacterial population on skin,
Commensals — organisms that reside on our skin, deriving benefit from us, but we do not benefit from them.
The majority of microorganisms on our skin are commensals, as they infrequently cause ill health.
Commensal microorganisms can prevent colonisation of pathogenic microorganisms.
So in one way commensals are beneficial.