Melanin has about a 30% absorption rate of ionizing radiation in the gamma spectrum, and remains stable (not oxidized in the traditional rate) while producing a current. The fungus is able to produce an acidic fuel source from the current that it feeds off of. The fungus is definitely breaking down radiation, incredibly, but it's mechanism is very poorly understood.

The fungus is (apparently) absorbing the radiation and using it as an energy source. But it is not making the radioactive atoms decay faster. So the time we have to wait until the area is safe and has a low radioactivity level doesn’t change.

True, but a layer of fungus would presumably act as an insulator, as it's absorbing part of the radiation? Perhaps it would be easier/cheaper/prettier to cover the sarcophagus in the fungus than in more concrete? Depending, of course, on a) how much it actually absorbs and b) how thick you can pile the stuff?

Nah, when gamma photon is absorbed it doesn't matter whether its energy will be used for fungal metabolism or converted to heat right away. And in case of gamma absorption rate mostly depends on mass density, so fungi will be likely as good as water. Concrete not only absorbs more radiation for the same thickness but is far more stable than anything alive.

what about the toxicity of the water as a result of being exposed to radiation, versus the toxicity of the fungi?

I'm not a nuclear scientist, but I can't think of any way pure water may become "toxic" due to exposure to radiation (instead of dissolving radioactive materials, which would definitely be a problem). Maybe excessive neutron radiation could build up tritium, but that already sounds like a stretch. (Most radioactive elements don't emit neutron spontaneously.)

Whoops, you're totally right! I misread the comment I responded to. Melanin is only useful when radiation is emitted. It can't coerce decay to happen more quickly.