If it were my tree, I would cut out the damaged root on the left that is closest to the trunk, or if it is fused to the trunk I would at least make a cut at both ends of it. I would also cut out the 2 roots closest to to the trunk on the right side (the one that looks almost vertical and the one in front of it.) I would also snip those 2 very small pencil sized roots at the very bottom of the photo. A tree that big that is healthy should be able to handle that, and I would feel a lot better about it's future.

This is what happens when root issues aren't corrected at planting time. Your tree could be the poster child. Not an accusation - just an observation.

I would correct anything you find that isn't radiating outward from the bole. It doesn't all have to be done at the same time. Do the worst first. All the roots that close to the trunk are plumbing (conducting roots) and anchors, so there is no harm in digging down a foot or so to get a good look at what you have to deal with. You might map what you find that needs attention, so you know where to dig in future years to make corrections.

There is no question that the tree's future vitality, it's ability to realize it's genetic potential, and its life span will all be limited by what the picture reveals.

Al