That's the case with any stream ecosystem, with blackwater there are very few plants to help with nutrient export.
Yes, but the differences between a typical forest and a rain forest are many.
As little as 2% of sunlight ever hits the rain forest floor. The average temperature is 27C and because of the high annual rainfall humidity is high. The temperature, lack of sunlight and humidity all contribute to rapid organic decay and the rainfall quickly leaches the released nutrients. The heavy annual rainfall also imparts a fairly swift current to these blackwater environments quickly flushing any leached nutrients farther downstream leaving the blackwater nutrient poor.
In the video that you posted several things are noticeable: a substantial layer of organic matter in various stages of decomposition, a lack of green periphyton (which translates into low Oxygen levels), and a fairly high TSS.
Blackwater streams are also very acidic, low or entirely lacking in KH and GH and have a very low level of conductivity.
I found this definition to be quite useful-
"Black-water rivers. The water in these is brown and rich in humus. Its
transparency is only about 1-5 m, although there are no significant amounts of
suspended inorganic particles. The brown water is always very acid (ph
3.7-4.7) and poor in inorganic ions. The humic substances--either dissolved
or colloidal--are linked with a special soil type, a tropical lowland podsol.
which is a bleached white sand covered by the Caatinga forest of the Upper
Rio Negro."
River Ecology, B.F. Whitton
Truly recreating and sustaining all of these required conditions in an aquarium environment would seem to be quite a daunting challenge.