IT Operations lives and dies by all the “5 minute real quick” tasks. The fact is that many requests fall into that category, but there can be 100s of those per day. The only way to manage that is by forcing people to open tickets, and then handle them according to priority.
Triage is incredibly useful in life and death situations, and has some value in many others. Sticking to unmovable policy no matter what however is not IT Support, it's Corporate, Faceless IT Support that makes everyone who isn't IT dislike us.
The world doesn't have to be this way, and rigid adherance to policy and your disparaging attitude are some of the main reasons I hope I never have to work in soulless corporate IT again.
As with all the other criticism in this topic, the fault is with the execs, and not the frontline IT workers.
Running a tight ship may not make everyone happy, but it does force people to prioritize what really needs to get done vs what’s not critical.
The only way they are being unreasonable is if your company is in the high single or low to mid double digits of employees and they are using it as an excuse to avoid work. For large companies, there's enough trouble with managers and officers of the company all thinking they can just take an IT worker at their pleasure regardless of other workload, so they're probably going to be extra defensive for anyone else.
You should work IT servicedesk for a few months for a large company that doesn't want to plow money into IT and see how it is.