If you must exist in this kind of organization use this to your advantage. Get involved in important projects, setup purchase proposals, then make sure you add in new laptops, cables, mice, extra monitors, and whatever other accessories you need. Do you have a remote KVM attached to all 100 servers? Yes. Will finance care if you add 100 monitors, keyboards, mice, etc? Nope. Will your vendor happily add those on to the price? Yup. How do you get involved in projects? Find a Director or VP who wants to get something done and say "yes" or "we'll find a way" to whatever it is they want to do. Then do your research and give them a proposal: "We can accomplish X in 24 months with Y headcount and Z equipment budget". If you can cultivate a reputation as someone who "gets things done" eventually you will find the normal rules no longer apply to you. Finance will stop asking questions about your projects.
You have three rational choices: 1. Play the game, 2. Keep your head down, 3. Quit and move to a company that doesn't play those games.
Sitting around complaining that a big company has crappy inefficient processes is like complaining that water is wet. A complete waste of time and makes you look incompetent to other people in the company who are playing the game. These inefficient processes end up optimizing for people who know how to talk the code and cultivate the right relationships. Take advantage of that.