I totally agree that it's ridiculous and sucks to do, but that also sounds like incredibly high ROI on your time.
Spending a month filling out paperwork to save every dev in the company 15 minutes a day or whatever would be a massive win. Like an "I deserve a promotion" level win.
I get what you mean, though. I've fought to bring products in a couple of times, and it's one of my least favorite tasks. It's endless meetings, and nobody on the other teams is super helpful because they're not going to get a bonus if this works out.
Edit: Another thought; spending your time making procurement easier might also be a worthwhile endeavor, if you could get the buy-in from someone that procurement will listen to.
- it costs them nothing to 'reach out'
- your company might not be so bureaucratic
- you might be willing to set up shadow IT (run software without permission)
- you might move to another company that is more permissive
- they might be able to roll up developer interest into an enterprise-level sales pitch
As far as risking being annoying, it's an unfortunate reality that you come out way ahead in sales if you talk to a lot of people, even if you make a fraction of them hate you along the way. That's even true when selling to programmers. But it does have externalities as all the sales teams collectively evolve their tactics to keep cutting through.
So I'd really rather most didn't come to that realization. And, well, we as developers do have some influence.
You may have side projects as well.
Also there's tools that are borderline personal, some I use or used: Quokka.js, GitKraken, GitHub Copilot.