There could be many factors such as new building areas, landscape areas, proximity to the house/structure, excessive pest problems.
In the building areas you want to remove all woody debris because of poor compaction.
In the landscape area you would want to remove the stump if you plan on replanting, putting up fences, pouring concrete, putting in children play areas, planting grass, etc.
The proximity to the house or structure is important because certain tree stumps will still grow; if the stump continues to grown it could cause structural damage. If there are stumps left this would create a new home for pest/bugs.