Reasons for an academic to need administrator rights on work computer
So far, I have only come across one reason for needing something close to administrator rights on a fixed department machine: using scientific software.

When you start using a new scientific piece of software, you often have its source code, and need to build it first. Typically, there is no documentation of what exact packages in your Linux distribution are needed (as this changes over time, and there are many Linux distributions as well). So the process is:


Try to build
Identify the cause of error (installing new software, updating the compiler, ...)
Fixing the cause of error (requires administrator rights
Repeat steps 1-3 many times until done.


You can only move towards the respective next issue when one has been resolved. It is unrealistic to assume that you can give an admin a list of required packages upfront, 

Without admin rights and an admin reaction time of, say, ~6 hours, this process may easily take a week. With admin rights, the process will be much faster.

BTW: When you start using scientific software professionally, there may be more packages that you need to install (LaTeX, screen, ...), so the process continues.

If you tell the IT people that this is the (unavoidable) process with most scientific software, and you will need to work with ~10 such tools during your PhD, then you should have a good point. On a technical level, there may also be the possibility for "admin light" access, namely by whitelisting your username for "sudo"ing a package installation request. Perhaps that is an option as well in your case.