Not sure about tannin leeching, but you can get rid of a lot of tannins by pre-soaking your soil and doing a lot of water changes. I am doing a dry start Walstad tank currently, and I pre-soaked my soil for 2 weeks and did water changes in the bucket it was in every day. Cleared up a lot by the end.
If you plant heavily enough the roots themselves release oxygen into the substrate which also helps deter/stop anaerobic bacteria.