You have four choices, none of which are easy for the situation you're in.
Fix it at the server level
Ban every workstation under the purview of the person violating your security policy. What's the point of security otherwise?
Fix it at the client level
Take away root. Period. Anything short of this is a paper thin sleight of hand that will be worked around every time.
Burn it all
Implement a network filesystem with user based authentication. This is a complete redesign which will involve reconfiguring both the server and the workstations. (read: low traction)
Some people like to watch the world burn, others aren't given a choice
When faced with an employer that doesn't want to do the Right Thing, sometimes you have to let the fire burn itself out. If you're not allowed to perform your job function and curate the security of the networked filesystem, you may have to wait until a large enough security violation occurs that can be used to drive the point home.
This isn't the same thing as apathy. An apathetic sysadmin doesn't care. You do care, but occasionally it's necessary to let your employer feel the natural consequences of ignoring a problem. It's important to distinguish between the two, and this is a career skill. Pain is part of the healing process sometimes.
If you know someone who carries some weight whose files are located on an accessible NFS share to one of those servers, you may be able to make the point sooner with a private demonstration. The share in question doesn't have to be mounted by default, it will be enough that root access on one of those workstations is providing vector into files people have no business in meddling with.