The biggest problem is that most crawl spaces were constructed to be vented. While building code calls for vented crawl spaces for air drying purposes, this is harmful to the home. Because of The Stack Effect, air circulates through your home from top to bottom, like a chimney.
In winter, rising warm air increases pressure at the top of the building, which pushes hot air out at the top and sucks cold air in at the bottom. The reverse occurs in summer, when cool inside air tends to get pushed out at the bottom, which draws hot air in at the top. This ends up creating a comfort problem that feeds on itself, moisture damage, and energy loss. (Source: Pro Remodeler)
As hot and humid air contributes to high levels of moisture and humidity in the crawl space and home, this can lead to sagging, soft, buckling floors above, and result in problems to hardwood floors. Similarly, cold wintertime air that is vented inside will make the above floors feel chilly and overtax your furnace. (Additional resource: Liabilities of Vented Crawl Spaces, Their Impacts on Indoor Air Quality in Southeastern U.S. Homes and One Intervention Strategy).