Isn't the large total surface area of the asteroid belt overwhelmed by drawbacks like unusability of most of it for most purposes (uneven, unstable, unshielded, etc.), and the fact that humans do really poorly in microgravity?
Freeman Dyson's the person after which the Dyson sphere is named, so the current (relative) "unusability" of asteroids or the fact that humans currently seem to "do really poorly in microgravity" are 'just' additional obstacles to be overcome sometime in the future from the perspective in which space megastructures are possible.
But yeah, I don't think "surface area" is the right angle to look at. More like "volume within a sufficient depth". A lot of (most?) asteroids and comets consist primarily of water ice, and water happens to be pretty darn good at radioactive shielding, so if we build habitats inside the asteroids we'd have a solid chance of significantly addressing that particular hazard (and also have plenty of water for drinking / agriculture / fuel).