Your post is both depressing and familiar. I think the reasonable long term solution is that each dev team have one admin as well. That way you have "your guy" who knows what's going on with the code being developed/deployed.
I'm not sure if there would be enough work for a full time admin / team so maybe one admin could be shared among two or more dev teams.
That's how it starts. The scenario goes something like this: Central IT is not responding in a "timely" manner. Bosses meet, but no common ground is reached. <INSERT BAD EVENT HERE> Developers complain to Boss that they are not to blame. Boss goes to his Division Boss. Higher level boss disagreement. Division Boss gets his own admin and servers. Central IT is no longer the only IT as Divisions now have IT. < TIME PASSES > New plan to centralize all IT. < CYCLE REPEATS >
I'm not sure if there would be enough work for a full time admin / team so maybe one admin could be shared among two or more dev teams.