Creating new database connections is expensive as it takes time.
Creating them when a request arrives will delay the response, so it is good to have them created before the request arrives.
It can also contribute to a https://en.wikipedia.org/wiki/Cache_stampede[stampede effect] where creating a lot of connections in a short time makes things worse as it slows down the system and blocks threads.
Closing a connection also invalidates all server side statements caching for that connection.

For the best performance, the values for the initial, minimal and maximum database connection pool size should all be equal.
This avoids creating new database connections when a new request comes in which is costly.

Keeping the database connection open for as long as possible allows for server side statement caching bound to a connection.
In the case of PostgreSQL, to use a server-side prepared statement, https://jdbc.postgresql.org/documentation/server-prepare/#activation[a query needs to be executed (by default) at least five times].

See the https://www.postgresql.org/docs/current/sql-prepare.html[PostgreSQL docs on prepared statements] for more information.
