I’ve yet to see someone tell me with a straight face that they hold any value like what we want them to be.
That agile estimation is fuzzy BS is a certainty. But it's a nice comforting blanket to help clients accept "we're just gonna start working on this, if you decide you don't want us to work on it anymore tell us to stop," which is important because that's the most cost-effective way for the client to spend their money, in many cases.
It's nowhere near as accurate as anything resembling an actual engineering estimation process, but ain't no-one got the time/money for that. It's probably a little better than the seat-of-pants "just give me a ballpark right now (but I'm totally gonna hold you to it, gee isn't it weird how we're always fighting fires and in crunch mode?)" that it's replacing as far as accuracy, but more importantly it makes that crap not happen (assuming it's functioning correctly).
BTW, you forgot the part about giving improving metrics to satisfy management and maybe get a raise (vs 100% not getting one), or a nice story line about how you managed to improve team velocity YOY by 50% through magic on your resume, which in the same way is "reducing an engineer to a few quantities" and equally "turns my stomach" as for alexandercrohde. Most of the things I've done to introduce improvements are immeasurable because they're changes that are mindset shifting or technological leverage therefore there is no metric associated because of the pervasiveness of their effects.
† if you're doing, say, 10 push-ups, instead of "1, 2, 3" try counting each number twice, like "1, 1, 2, 2, 3, 3". Magic, you've done 20. You know it's a mind trick, but it'll still work.
†† Going from email+phone+hallway communication, silo'd knowledge and SPOF Bus Factor to a serious issue tracking, knowledge sharing, and automation on GitLab. Going from manual machine building to fully automated system provisioning and one liner deployment. Any associated metric would be either completely immaterial (e.g confidence and well being) or produce an off-the chart ratio (just computed one just for fun, that's a ~1800% improvement in human cycles — not even counting failure modes — it's so beyond ridiculous it doesn't even mean anything).