Surface roots on some trees such as maple and oak normally go deep into the soil when possible – and when required because of lack of “surface water”. If you have a high water table in your area, then the roots are prevented from going down because, strange as it seems, the roots won’t go “into” water. That is, the root system needs to transport water to the tree canopy, but the roots will rot if they’re in water. So they spread out into the “normally dry” soil and pick up moisture there. Obviously, a rock ledge or other impermeable strata in the soil can prevent deep tap roots, too.
When the high water table (or rock ledge, etc.) in the soil prevents the roots from going downward, they spread outward instead. This makes for a potentially unstable tree. That is, likely to blow down – or even simply “fall down” – at some point.
I’m not saying that’s the only reason for a tree to have surface roots! But it’s a very common reason, and worth looking into.
I’d call that arborist if I were you. He may advise that the tree is already unsafe and should be removed.
I like older trees, too, and keep them whenever possible. I also have a very large oak near the street end of my driveway. Fortunately, there is zero surface disruption from the root system, and this tree has been well tested with wind and snow loading. I’ve seen other trees in my neighborhood that did fall during our early, wet snow last October. Trees with 2’ diameter trunks simply fell over – and they often had the type of shallow root system you’ve described.
When I was much younger we had a “swamp maple” next to our summer camp. That thing had a trunk that had to be over 3’ in diameter. One winter it simply toppled into the neighbor’s yard (fortunately it fell between their house and garage). Because of its location on the low point between the two properties (next to where we used to have a well, in fact, that was only about 6’ deep), it also had a shallow root system.
I’d definitely look into this if I were you.