For these political reasons, it's important to have executive-level support, or else it would never fly. My first job out of school was doing exactly as the gp suggests at a national telecom. Job-shadowing people in their day-to-day work, understanding their problems, and turning around web/desktop apps within days or weeks to solve their problems. We had huge success. We won an international award for what it's worth (Stevie Awards for Best Support Team). We saved our company millions, and were one of the keys for the company to survive a big labour dispute. Can you believe that previously, for a national telecom, all orders for corporate telecom solutions had to be gateway-checked by a single person? We democratized stuff like that so that processes could be much more flat. No need for requirements documents, no change control, complete freedom of creativity, complete freedom to decide what work to accept, etc. I know how that's sometimes necessary for big projects, but for small high-ROI stuff, it was beautiful.
The other side of the story is that we ran into huge political problems. Every day, someone was trying to kill our team because we were making the traditional IT groups look bad with our turnaround time and solutions that worked. On the other side, we were automating things that people didn't want automated. If we didn't have support from the CEO down through a specific chain of command, we would have been killed within months, if not weeks. We didn't even call ourselves developers. Our official position title was business analyst because then IT would bug us less. We weren't even part of the official IT department because those guys couldn't get outside the box. So we were just a small group of business analysts who tried to hide until we were too successful to hide anymore. That's when the attacks really started coming. And then we continued to be successful, and then they started trying to copy us instead. Last I heard, that team's unfortunately been swallowed up by the bureaucracy now, and is a shadow of what it once was.
Fascinating experience.
edit: added end of the story