I've never cleaned anything after brewing teas. My air stones have been almost solid brown. My cheese cloths I've just dumped the contents out then reused. Like when you ferment and reuse your germ to get the fermentation process sped up. For me that's added microbial life.
Through veg almost every watering I give is some sort of tea or organic watering. Fulvic acid, worm juice, fish poo, mycorrhizae, kelp meal, alfalfa meal sure I'm forgetting something. My plants love that, you're right it isn't needed they'll still be okay but man they look happier getting those organic waterings. The only reason I dont use teas more in flower is because of top feeding high amounts of slow release fertilizers