Bottom line.
Media has surace area to grow nitrifiers.
Nitrifiers grow best with full oxygen saturation, or in the case of the Voodoo Shower, supersaturation.
It will work at a drip trickle, submerged media( well aerated water) or a blasting shower media.
I'll tell a secret. I have BH media running in 2 canister filters doing 150 gallons of aquarium water.

It performs admirably... just like cheap ceramic donutz.
NO. I didnt buy it !
By design. The BS,,, I mean BH

media can handle a more violent flow of water than say, a ceramic donut or little green army man or pvc strips or strapping tape or...
Matter of fact its about like Lava rock !.... which is $600 for 18 YARDS.
If you had an airstone in a casket under ground the results would likely be the same.
If you look at REAL water treatment...as in human waste conversion, you'll see a slow rotating, huge spraybar spreading the water which has had the solids removed over far infra... I mean ceramic media as it goes around and around 24/7.
The water then gets pumped back to a tank for bacterial analysis and treated there, as necessary.
The one I'm familiar with is a 300 foot circle with a 300 foot spraybar pivoting from the middle.I'd guess it makes a complete circle in ??? 3 minutes ?
The media is about 4 feet deep.
The pump is a 35 horse electric so I'll take a wild guess at 3500 gpM, which is about what my buddy runs at the striper farm.
They have the place locked up with heavy security so I'm not sure how many Nexuses with answers it takes to remove wastewater solids from 175,000 homes a day, before it reaches their Caca Showwerz.
The bottom line is solids removal before bacterial filtration so most any setup can, and will, work.
Maybe we could get Koiphenator to fill his stream with BH and bypass everything but his drum filters and give it a whirl ? I'll betcha it'll work just fine.
Sorry for the Momo~Blasphemy

PBUH..................zzzzzzzzzzz