Been having conversations like this with a client I've worked with. They get approved by corporate for us to use claude and ask how much faster we'll be able to move with it.
I tell them "Us engineers will probably be able to deliver some of our stuff faster but it won't have even a slight effect on the actual deliverable because we've never been the bottle neck", it's the fact that the process to get an S3 bucket allocated takes (not exaggerating) 4 weeks there.
This matches my experience. My previous position was at a FAANG and sometimes getting a VPN link setup for a new host would take a month of approvals.
Writing actual code was maybe 10-20% of what I did. Most of it was meetings, design review, authorization requests, etc