Server side antivirus or not?

So in this sort of "protected" private datacenter scenario where 95% of the users access the servers from client tools, and there is little to no public exposure, is there a strong case for running A/V clients on all of our back-end servers?

Not really, no. Though, it usually boils down to an issue of "compliance" or because someone high enough up thinks running AV on all your private servers is how "security" is created.

Having said that, it's not a bad idea to have at least occasional anti-virus scans on all your machines, regardless of how well-protected or isolated you think they are, and there is a strong case to be made for this practice.

Coincidentally, the easiest way to achieve regular AV scans on all your machines is to have a lightweight AV client installed on all your machines. (Again, "all" means "all" and includes the "protected," "private" servers you mention.) Once you accept that all your machines should have an AV client, it's down to an issue of configuration to prevent the AV clients from interfering with your servers.

Personally, I prefer to handle this by having an AV client on all my servers, and disabling the realtime protection/on-access scanning portion on all the servers for which it is safe to do so, while leaving the scheduled virus scans intact (or adjusting the schedule as needed). This strikes a balance between server performance and virus protection. Servers that are heavily interacted with by the users or connected to the internet get the full AV policy, of course.