We’ve done it both ways with the many large trees we’ve had to take down on the property. Grinding the stumps will 100% definitely create a large depression over time – a few years-- as the stump rots. All the compaction in the world won’t save you. Every place we cheaped out and had the stump ground, after 3-5 years a big circular depression has formed.
If this were just in your yard, I’d so go for it because you can always bring in a load of topsoil to level the ground. But not when there’s going to be expensive arena footing at risk. Tell your wallet I’m sorry, but pulling the stumps for a large tree is the way to go.
