You think the filters should be cleaned weekly? That is radical thinking. Even the manufacturers of those cartridge filters don't recommend that kind of frequency, with Tetra and Marineland recommending once a month. I'm sure you don't use cartridges (as I don't, except to use them up when the filter is new) and probably have alternating filters, however I don't see a great benefit to cleaning the filter this frequently. One week old filter media is hardly dirty at all in a reasonably stocked tank. Additionally, in a tank with only one filter, I can see the beneficial bacteria being upset by being rinsed four times a month.
The media we use does filter out some dissolved organics (the ones we can test for) but definitely not all...hormones and metabolites are still in the water column until they are diluted with fresh water. Refreshing the water frequently also adds back the carbonate salts an aquarium needs for stability. Also, frequent water changes trigger breeding in many species. So there is definitely more to it beyond just purifying water.