Very interesting! I did some poking around and found this related study on clinicaltrials.gov:

Gargling and Nasal Rinses to Reduce Oro- and Nasopharyngeal Viral Load in Patients With COVID-19

For this study, 48 patients who have been diagnosed with COVID-19 will be randomly assigned to four study groups: control, saline, chlorhexidine gluconate, and povidone-iodine. Each patient will be asked to gargle with a solution of either saline, chlorhexidine gluconate, or povidone-iodine or nothing (control group) as well as spray the same solution in their nose four times daily. Patients will then be tested for COVID-19 once daily in the evening for 7 days and viral loads will be measured.

Notice the dates on this, a start date of April 2020 with completion of May 2020. Cheap, fast, simple study, right? Well, this one was canceled.

Granted, it could have been canceled for all sorts of reasons. It may have been redesigned and launched with different criteria. It would be nice to know why.