I honestly have to wonder why we don't have robots doing the majority of these tasks. Obviously, a robot couldn't troubleshoot detailed or obscure problems, but for things like provisioning a server, rerouting around bad network hardware, replacing drives, NICs, etc. they should be good enough. CERN already uses robots for the LHC tape backup system. I can't see that this would be that much more complicated.
Humans are very easy to train compared to robots, and aren't that expensive. I'd imagine each facility is laid out slightly differently, with different generations of hardware. To make the robot work well you'd either have to program in each hardware variation or make the software sufficiently advanced to understand the differences itself and adapt. I imagine the cost/benefit wouldn't pan out when you look at how many datacenter techs you replace with how many software and hardware engineers.
Humans are great at adapting, so if you throw a new enclosure at them or a new motherboard design which has the CPU sockets in a different location, they'll be able to learn the new system in 30 minutes.
A former coworker of mine trained to work with factory robots, but he realized that there wasn't much of a current job market for it because humans are still way cheaper (and will be for some time). Instead he went into software.