You argument is essentially hanging on the assertion that the first number an employer would offer is also the maximum number it could offer. I know exactly one company that operated like that: they'd make the maximum offer and if you did not like it there was no further negotiation. Most companies don't do that (neither does that one any more, the CEO who had this policy had retired a while ago).
What I've observed in my experience is that most companies will try the minimum offer regardless if you tell them your requirements or not, which makes sense since they do research too and unlike yourself their HR has much more experience and data for that. If you were asking less than the minimum they were willing to pay they will likely still pay the minimum as the sibling suggests, there is no point to save and get to hire again for the same position in a couple of months.
I think it's an illusion people get when they ask for a number and get it without much fuss. It makes them think they asked too little but in reality the hiring manager had the range like 200-250 and you asked for 210. Why would he bother to try to push you down to 200? On the other hand, why would he offer anything other than 200 if you did not ask?
What I've observed in my experience is that most companies will try the minimum offer regardless if you tell them your requirements or not, which makes sense since they do research too and unlike yourself their HR has much more experience and data for that. If you were asking less than the minimum they were willing to pay they will likely still pay the minimum as the sibling suggests, there is no point to save and get to hire again for the same position in a couple of months.
I think it's an illusion people get when they ask for a number and get it without much fuss. It makes them think they asked too little but in reality the hiring manager had the range like 200-250 and you asked for 210. Why would he bother to try to push you down to 200? On the other hand, why would he offer anything other than 200 if you did not ask?