As shown in the sequence of photos in
this link,
killing all the algae when shocking a pool is not normally the most time consuming part of the process. Notice how much of the floating algae in the pool gets killed and falls to the bottom after 10 minutes. What takes a long time is the full filtration of large algae clumps if people do not vacuum-to-waste and the more complete oxidation and filtration needed to get the water from cloudy to clear. This latter stage is the longest and varies depending on the quality of circulation and filtration and has nothing to do with killing the algae. In a cloudy (not green) pool after the initial chlorine shock, the algae has all died and the chlorine has bleached out the chlorophyll so what is left is to remove that organic matter from the pool, not to kill it (since it's now already dead).
Now if a pool has very high CYA levels, it takes extraordinarily high FC levels to kill the algae quickly so your system might be helpful in that case, but then you are still left with a high CYA pool and since the answer to that is water dilution, why not just dilute the water first to get the CYA lower and then shock to kill the algae? Also, once one gets their pool in good shape, the prevention with proper chlorine levels relative to the CYA level prevents algae growth so you don't get this problem again. That's the experience of most on this forum. They don't get regular algae outbreaks. The most common algae scenarios are for those who close their pools over the winter and don't close and re-open them while the water if very cold (< 50ºF). It's warm water situations with no chlorine where there can be a lot of algae on opening.
For a service tech, the more classic approach is to shock the pool with chlorine with the pump on, then after a short time add a good flocculant (e.g. OMNI Liquid Floc Plus) and turn off the pump. After overnight or from morning to late afternoon vacuum-to-waste and then start circulation again.
Now if you were to tell me that your oxygen system were to act as a super clarifier consolidating algae cells so that the water gets to crystal clear much faster, then that's something else though would need to be compared in cost to a good clarifier or flocculant or to
Adding DE to a Sand Filter.
Do you have photos showing a pool full of algae and showing what happens over time using your process? Perhaps that can help explain the situation better since a picture is worth a thousand words.