Work computer totally rekt. Force everyone to plug in their computers every night and force updates on them. You play with fire, you will get burned. Maybe they will reconsider such a foolish policy.
Discussion
The other option is to have users never update their machines. That's very, very bad. The issue here is your systems administrators not properly testing updates before deploying to production.
That is an issue as well. No doubt. But I see no reason they couldn’t allow people the option to manually do it and just send out a bi-weekly reminder.