Chinch bugs and sod webworms do not eat grass roots in the north!! Sod webworm does act as a cutworm in corn, eating roots of corn plants. Do they do damage this way on southern grasses?
The hairy chinch bug, common in our area, sucks plant juices. In doing so, it blocks uptake of water and downward storage of plant sugars. Therefore, chinch bug damage is generally considered fatal to the turfgrass plant. Whether to sod, seed, overseed, or just let grass recover on its own depends on the extent of the damages and the client's wishes.
Sod webworm eats leaves of turfgrasses. Since it chews leaf just above the crown, sod webworm damage is not fatal, because crown is not injured and can regrow leaves. But heavy webworm infestation, and continued eating of new leaves can cause the death of the grass plants. If the webworm damaged areas have not coalesced - you have individual brown spots - I would generally let the turf recover. But if you have a 100 ft² or larger of solid damage, it's time to consider seed or sod. Look closely for growth of new shoots for a couple of weeks after you are sure the sod webworms are controlled; if you see very little or no new growth starting, then help the recovery with sod or seed.