Hi Jay! Glad you found it helpful!
It’s tricky for me to give any advice on that matter — is very subjective, depends on your specific situation.
What you describe is very similar to what I heard from the recruiters — they will say there’s some team that approves the amounts, and there’s a threshold you’ve reached. It’s hard to tell whether it is true or not. But you are very limited in your options — give it or leave it :)
The point is that they do not hire specifically you because they want >you< so hard — they just want to fill an open position with an engineer. Did you speak with the hiring manager? Do you know what team is it? If you have access to the hiring manager, you can try to speak him to improve the offer, because that will create a situation where he wants you, specifically you.
As for the worthiness — you can refer to my previous reply to Anton. You can get some experience in Amazon, switch teams, but once you’re inside it will be time consuming to get a significant raise.