>> There is also soft, white, dry, matter around these roots
Once I used a cheap and harmful "soil amendment" that turned out to be mostly wood. Once turned under the soil, it made huge masses of white, "powdery" fungus that looked sickly and apparently sucked ALL the N out of the soil for a full year.
Some of the stuff between the roots might be fungus, as Leftwood said. I GUESS they aren't bad for the plants, but when my poor soil became 50-60% fungus all hopped on too much sawdust and wood shavings, nothing wanted to grow in that.
I suppose the problem was the too many wood products near the surface (not the fungus - the fungus was curing the excess wood).
It would have been fine on the surface, as top-dress mulch.
It would have been great if buried deeper - hugelculture in a small way.
But mixed with soil, the C in the wood stimulated very rapid fungal growth. All that fungus was starving for N, so the plants I tired to grow were double-starving for N (fungal mycelia are much better at extracting nutrients from soil than plant's roots).
I don't think your 'problem' was excess woody shreds in the soil, just a lot of tree roots and some fungus, just doing their thing.
In my yard, anything planted near a tree loses the competition to the tree. Even a compost heap was taken over by pine tree roots. No more compost, just feeder roots for a tree!
Well, ivy can compete with tree roots.
