But if you just compost the fungi, you are just back to where you started. With phytoextraction you have to incinerate the plant material afterwards. I know fungi aren’t plants, but similar principle.

You can harvest the mushrooms and throw them away.

The fruiting body of a mushroom often represents only a fraction of total biomass. It depends on the species, but what we see above ground is more analogous to a flower than an entire plant.