I've seen several studies on this, and most show that biobased filters can do a great job with algae. However, where they are lacking is pathogen removal. The biofilters can and do provide some sanitation. However, they do not work quickly enough to effectively sanitize, and their performance goes down substantially with bather load. Here is a link to a study of one of Canada's larger natural pools, Borden Park, in Edmonton:
Pathogen performance testing of a natural swimming pool using a cocktail of microbiological surrogates and QMRA-derived management goals | Journal of Water and Health | IWA Publishing. This is a quote from their summation:
"Overall, the individual treatment barriers performed as intended (
Table 2); however, due to the constant dilution of treated waters entering the pool post-treatment, it was demonstrated that safe levels (based on the key reference pathogen,
Norovirus) could not be attained at the 50th, 75th, or 95th percentile measurements of risk within 24 h. Further, our modelling found that treatment barrier log-reduction values in excess of ∼1.3 (see Supplementary Figure S1) provided little improvement on the amount of time required to treat the NSP waters to meet the 35 illnesses per 1,000 bathers benchmark. To mitigate health risks, the following steps were recommended: (1) strict preventative measures be taken by ensuring bathers understand the necessity for showering with soap prior to entering the pool, (2) upon entry, bathers asked to not enter the pool if they have been ill within a 2-week period, and/or (3) the maximum number of bathers allowed per day be reduced to <45 to maintain an acceptable level of risk."
Can natural swimming pools be safe? I think the answer is Yes, potentially. However, I think there are just too many caveats . For a smaller sized pond/residential application, you would want some combination of high replacement with fresh water, low bather load, and longish wait times between swimming sessions. Personally, I wouldn't be willing to make those sacrifices.