Many birds are critically dependent on a supply of inverterbrates to eat.
Many of these inverterbrates, especially during the leaner times of year, depend on rotting organic matter. The insects cannot eat dead wood without the fungi, because the fungi are required for the first part of the process which breaks down the wood.
No fungi = no food for the birds.
There is a little known connection here between the evolution of trees (i.e. lignin, which is what makes wood tough enough to support full-size trees), the evolution of fungi, and the existence of the enormous coal deposits which made industrialisation possible. It took several tens of millions of years after the first lignin-containing trees appeared before anything at all "figured out" how to metabolise lignin. Most animals still can't break it down. They depend on fungi to do this. But the fungi themselves took quite a while to invent the correct enzymes to do it, and in the intervening time, all of the dead trees just piled up on the ground and did not rot. The result was the massive coal deposits that gave the carboniferous period its name.
In short, even if humans wipe ourselves out and the earth is allowed to evolve without our input again, there will never be another lay-down of coal deposits like that, and the reason is fungi. Dead trees now become bird food rather than coal.