So I am bit confused but also intrigued by the concerns or comments, since you guys know a lot and I do not. So a few comments to what John and Randy commented:
1. I wanted to stop using Kalkwasser / calcium hydroxide and needed to offset the PH impact. Is not using Kalkwasser a good idea, that is part for a separate discussion. The PH impact from my current setup with a still rising 7 day PH average of now 8.33 (0.1-0.2 higher) outperforms the previous Kalkwasser method for my tank. Of course this only matters if chasing PH is your objective. It is mine
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2. The skimmer overflow scenario is very interesting, as I am not able to see in my setup how this can lead to a problem, but there are setups where this might be very well true. I am adding the drawing from the setup and it would be great to hear what needed to happen for this risk to materialize. Also, the skimmer has a shut-off valve if it overflows and a drain (which I am not using at the moment). Still, it was helpful as it made look at the setup differently, and I can see that if the simmer cup overflows (shut off valve not functioning), then floods the scrubber entirely, then the liquid from the flooded scrubber goes against the gravity (drawing is different from how I have it) into the silencer and back into the tank, that this would be not good or rather devasting.
3. The wastefulness of the media is another good point. It is still too early for me to determine how long the media lasts, and I hope with the recirculating setup its viability will be significantly extended.
4. The ATO intake would be a bit complex for me to setup because the hose is rather thick, but it would reduce the main painpoint which is that some skimmate enters the scrubber, and I do have to empty the water from the scrubber every 3 days, and would need to deep clean the scrubber when the media is due for replacement, whenever this is.
5. The two benefits from the recirculation is the high humidity that goes into the scrubber (can be offset with the ATO method), but also the assumption that lower CO2 rich air enters the scrubber requiring less effort by the scrubber media (at least this is my basic understanding).
6. In this setup, the skimmer lid does not have holes, it is completely closed. Which has additional benefit for the ozone (which will be a separate post).