As far as Systems Admins taking over sql server support duties, I think that can work as far as infrastructure and backups ( where backups are handled by something other than native sql tools ).

We've gone down that road twice, due to decisions being made by IT managers in the absence of any DBAs or DBA managers. The first time native sql backups and log shipping were replaced by Commvault backups administered by Systems Admins. This time we're headed towards Netapp snap backup and its not clear yet if the DBAs we now have will be involved in that or not.

Our System Admins have so far steadfastly refused to get involved in the nuts and bolts of sql server which means they could not manage maintenance like reindexing and update statistics in any reasonable way.