An IT department for a company of that size should have ironed out workflows and automated ways to keep tabs on who has what and who needs what. They may also be under various compliance requirements that expect due diligence to happen every quarter to make sure everything is legit from a licensing perspective.
Even if it's not automated, it's normal for a team to email IT / HR with new hire requirements. Having a list of tools that need licenses in that email is something I've seen at plenty of places.
I would say there's lots of other tools where onboarding is more complicated from a license perspective because it might depend on if a developer wants to use that tool and then keeping tabs on if they are still using it. At least with Docker Desktop it's safe to say if you're on macOS you're using it.
I guess I'm not on board with this being a major conflict point.