"Specify SQL Server administrators" - unusual default value
You're right: system administrators can gain sysadmin access, but you will find entries in the default trace for that action. Moreover, it requires restarting the service at least twice, which would hardly go unnoticed.

Not granting sysadmin privileges to BUILTIN\Administrators is a change introduced in SQL Server 2008. In my opinion it's a good idea: it allows the separation of duties between server administrators and SQL Server administrators. 

The main undesired effect of having BUILTIN\Administrators in your sysadmin role is the loss of control, which can manifest with one or more of the following annoying things:


New databases appearing on your servers 
Unwanted connections from windows admins that end up competing with legitimate connections
Implied permissions to windows admins on databases with sensitive
data 
Seemingly innocuous but disrupting "self service" operations,
such as taking full "one-off" backups on databases with differential
backup strategies.


Long story short, windows admins have a different skill set and a different mindset, not to mention different responsibilities: letting them manage your SQL Server instances is not a good idea.

My suggestion is to create a windows group for your DBAs and add that group to the sysadmin role upon each new SQL Server installation.