it depends a little on how your installation is setup and how you work.
For a university with a lot of users, it is probably more benefitial to do some thourough tests first in an test enviroment and see if the upgrade runs smooth and then upgrade the actual installation.
As I don't have the time and resources to do much testing and only few resources actually need to be moved, I rund usually the newest and the version before in parallel, with the older version running only old stuff and all the new things being implemented in the new version. So my old surveys don't need to be tested on the new server (as long as they are not running for a longer time or are repeated).
It works for me, it might be different for others. And the installation of a new clean limesurvey version takes about 5-10 minutes max. So you install it now and in 5 minutes you could import a survey from the old installation, check if it works and run it. So the "priorities" argument is also not too valid. Even if the IT guys need 1 hour to install, this is nothing that has to be argued about for long I guess. Lucky me that I can install the stuff myself and don't need to wait for some IT guy having the time (or better "is will) to install a new version.