Exposed tree roots

[BriGuy89]

...A Norway maple produces an immense amount of shade, to the point that no grass will grow (even hostas for that matter)...

It's not just the canopy at work -- Norway maples also produce a phytotoxin that eventually "poisons" the soil for other plants (but not Norway maple saplings) growing in the tree's area. That makes mulch the best and most reasonable option -- unless one wants to constantly fight with the tree for domination of the chemical balance in the soil.

 

[Hlakegollum]

I started putting mulch under just about every tree I have, large or small, based on the advice of our professional arborist who does our live oaks. It prevents trimmer damage, keeps the roots safe, allows the tree to draw more water instead of giving it all to the turf grass, and it looks nice if you do it properly.
And with the drought we had in South Carolina this past year, the mulch really kept stuff going on less water.

So do what the arborists say: leave the roots alone and use good mulch.

This is good advice, I was told years ago not to try to grow grass under trees. I would put down some nice mulch or a groundcover like ivy.