Amen, any TT or wet/dry ( which is what BH in trays is) will contribute three very important and often over looked things to a closed pond system:
1 ) it will increase oxygen levels so that the fish's metabolic performance is not hindered in any way ( aerobic metabolic activities and protein synthesis).
2) it will produce an overall larger water/atmosphere interface which will allow for metabolic waste gases to leave the system.
3) it will produce an efficient biofilm/nitrification ( again efficient metabolic rates just like within the koi themselves) without the usual limitations of submerged media.
If you then oversize the filters you are also expanding the overall water volume within the system. If a large % of the water at any one time is in circulation within the towers or trays, all the better.
( Notice I didn't take a shot at the magical rays! I'm maturing!

)
The kinder and gentlier JR