When I was at horticultural/agricultural college. I was taught that trees are in balance. What you see above ground is equaled by roots below. Obviously that doesn't mean it has the same 'shape or make up' but it does have the same amount of material. The roots are taking up a lot of 'ground space' They compact the soil, heave it up, remove nutrients and water. Should the roots come upon a void they will fill it up and then exert internal pressure on the walls of the void. I have see 'land drains' smashed by tree roots.. And when you concider that only 50% of the roots are inside the canopy 'drip line' the range at which roots can create damage is quite extensive. If trees are left to do their 'own thing' on a monument. it would seem very likely that they would eventually destroy it..
It doesn't take long for grassland to become a Forrest when left to it's own devices. 50 years or so if conditions are right. This can be plainly seen on some of our 'motorway' embankments and fringes. when they stop maintaining them in the late 60's the process began and now there are some pretty impressive trees and woods growing along these routes and in some cases woodland wild life corridors many, many, many miles long.