>
I get informed all the time on HackerNews that I cannot negotiate certain things. But I can, and do it all the time.That's different, and yes, you should absolutely negotiate! Their policy has them offer you below what they are happy to pay, well below what they are willing to pay. Do some research first, pick comps like a realtor picking houses. Understand you're on the sell side, so pick defensible and high comps.
Most likely, they didn't really pick comps, because the people who set their pay bands don't know that the consultant market data about tech jobs includes your uncle's other nephew that fixes computers at home, and a lot of other classes lumped in by job classifications, so the numbers they think are true are .. half? .. what you could make at a good shop. So again, choose well and defensibly.
Now the tables are turned, information asymmetry is in your favor. If they were lowballing, they'll come up easily. If they were stuck in a pay band, you're enabling them to get unstuck, which helps them and you. You have a valid pay scale, it's not about whether they evaluated you well during interviewing, its about whether the company is hiring well. In this situation the hiring manager probably has gathered their HR team is trying to make them under-pay, you're probably the nth candidate asking for more than they were told to offer -- but you're the first to bring them the proof points. They now go have an internal fight, better armed, and get you paid. Maybe.
But to be clear, YES - NEGOTIATE. :-)
For what its worth, this also works of course at the car dealer, but also at, say, BestBuy, or retail clothing stores, or most anywhere incentives can become aligned.
PS. Contrary to your characterization of my thinking, I never thought like you used to think (wink), as I came of age in Africa myself. All prices for anything in both directions were fluid and dynamic. So I came back to the US and just said "here's what I'll pay" and it worked.