This thread on this forum talks about the main downside to using hydrogen peroxide which is wear on certain spa components.
As for why hydrogen peroxide is not approved as a disinfectant by the EPA nor by Health Canada,
this paper showed that even with 150 ppm hydrogen peroxide concentrations there were very low reductions (26% to 61%) even after 30 minutes of
Escherichia coli,
Pseudomonas aeruginosa,
Staphylococcus aureus, and
Legionella pneumophila with no reduction in
Candida albicans. This study did not show silver ions used in conjunction with hydrogen peroxide helping very much while
this paper showed that hydrogen peroxide in combination with silver was effective at preventing uncontrolled bacterial growth (that's different than a fast kill). Both of these studies were in pools while the hotter water in spas would be expected to increase the effectiveness of the disinfectant.
As for Australia, it is
Poppit Sanitiser which is approved in Australia to be used in pools and spas at 100 ppm hydrogen peroxide.
In practice, since the hydrogen peroxide does appear to prevent uncontrolled bacterial growth even though it does not kill fast enough to prevent person-to-person transmission of disease, there is lower risk in a residential spa where you control who goes into your spa compared to commercial/public pools and spas where one sick person can infect many others.