General thoughts:
Cancer patients—in particular those with blood cancers—are routinely immunocompromised and put on antibiotics. Any potent effects would almost certainly have been realized by now. There are a lot of people who have made their careers by tracking what therapies work and which don't—and that includes controlling for "confounders" like those given antibiotics, etc.
Oncotarget isn't a bad journal—and this is certainly a good idea which may have applications we can't quite imagine yet. But it's unlikely to be a potent cancer therapy.
Getting rid of the CSC's is great for stopping the formation of new tumor-forming cancer cells, but you still need to kill and/or remove all the existing cancer cells.
So, this could treat the cancer stem cells as if it were an "infection-vector," but you'd still have to stop any current "infection" to save the patient.
This wouldn't really help late stage or aggressive types, but could make treatment efficacy better for cancers in early stages since it may help remove the cells that help a cancer come out of remission.
Maybe people with higher genetic propensity for covered cancer types could rotate on these drugs on a regular basis to reduce their risk? The eternal z-pak... Be interesting to see what the epidemiologists and actuaries come up with to assess the cost-benefit. Consistent anti-biotics would accelerate incidence of anti-biotic-resistant infections. There is no zero-risk since you can't actually take these drugs constantly. A tumor-forming cell could be produced between cycles. The long-term effects at such dosing levels were likely never studied and side-effects could be problems.
More likely, this would become one part of the full-court-press applied to treatment regimens.
Oncotarget isn't a bad journal—and this is certainly a good idea which may have applications we can't quite imagine yet. But it's unlikely to be a potent cancer therapy.