I work in Change Management for a major telco, I chair the IT CAB, and I oversee server and client patching (amongst many other changes!). When we patch clients, we are patching up to around 30,000 real and virtual desktops - when we patch servers, they also number in the thousands.
There is no way we would allow a sysadmin to patch anything at any time without some level of oversight, an individual admin has no oversight on other patches, hardware interventions, application releases, network upgrades, business campaigns, etc that may be happening on our environment at any given moment (this isn't their job to be keeping track of all of that info). For server and client patching is as light as possible, but we still maintain a close oversight.
On the Wednesday following the second Tuesday of each month (for example), I sit down with the Windows server guys and the Windows client guys, and we review their proposals to patch - usually we have a fairly rapid timescale that we can meet to ensure that the patches are deployed (including pilot testing, etc to catch any issues before everyone's desktop is broken!), sometimes there are other major interventions that overlap, and then we need to make prioritisation decisions and decide which has priority. We have made similar agreements with the Linux teams, where they have a special process to patch, and we have close oversight on Unix patches, as upgrading these servers with a reboot can be a very big deal.
The last thing you want is an application version release of a critical ordering application happening at the same time as a system software patch, and then to have an issue afterwards - is it the application version, is it the systems patch, was there some conflict with the activties being performed at the same time? Troubleshooting gets more difficult, teams point fingers at eachother, and the whole time the business is screaming blue murder.
Of course in an Incident situation there is more flexibility to get things fixed fast, and with security issues I am keen to break open the S-CAB process to expedite a rapid approval flow to ensure that security holes are fixed as fast as possible - of course most changes are encouraged to follow the rules though, the change calendar is published, and everyone knows when the "standard" slots for deployment are, and if most people manage to schedule their changes within those windows, then it minimises potential conflict for everyone.
Change management are not your enemy, they are your friend - once you register your change with them, they have your back, they will guard from other interventions clashing with you, will stop you from inadvertently upsetting the business, and will decrease change related Incidents. However, with great power comes great responsibility, and Change Management need to find the right process for the right type of change - we cannot have a full in depth investigation into every configuration change, every patch, every bug-fix, every new server to be provisioned. A good Change Management team will guide changes to the appropriate flow, and grease the wheels for certain types of interventions - it seems that the CAB mentioned in the summary are still finding their feet a little, and I am sure they will evolve over time as they start to understand which changes are high risk, and which can be allowed to pass with a lighter touch.