AUTO_CLOSE in SQL Server

The problem, however, is that there is minimal cost and overhead associated with not only tearing down existing connections, file-handles, and buffer allocations in order to 'shut down' a database when it auto-closes, but there can also be significant overhead involved in spinning a database back up when it's accessed by subsequent applications or users.

In fact, if you think about the benefits of how SQL Server connection pooling works from within .NET applications – the entire purpose of connection pooling is designed to amortize the COST of making expensive, initial, connections to SQL Server databases over multiple requests.