> I, for one, tell the number, which if was given to me during negotiation would result in acceptance on my part.That's not the same as saying you would refuse any offer for less. So you haven't answered the question I actually asked.
> I have not hypothesized the range
Yes, you did. In the scenario we're discussing, you said the manager's range is 200-250.
> this is the hypothesis, not the actual range
In other words, you're moving the goalposts. Sorry, not playing that game. Of course you can make up any numbers you like, but at the end of the day my argument is still the same: it's to your disadvantage to anchor the conversation on a number first. And you don't have to: as I've pointed out in another subthread in this discussion, if the company genuinely wants to hire you, at some point they have to commit to an offer. You don't; you can always go away and talk to someone else. (If you object that you might not be able to, my response is that you're already assuming you might get a better offer, which means you're assuming you can go away and talk to someone else. See further comments below.)
> It's trivial to raise it if you suddenly decided you can get more
I don't see how. You've told them you'd accept an offer from them for 210, but now you're reneging. The fact that you might get another offer for more than 210 is a reason not to tell them the 210 number at all. It's not a reason to go back and revise the 210 number afterwards if you get a better offer.
> This is why negotiating down from already satisfactory for both sides comp is a bad strategy for the HM.
You're assuming that the company will interpret your giving them the 210 number up front as a sign that your negotiating position is strong. I think they will assume the opposite: that your negotiating position is weak. Someone who already has good offers on the table, or expects to get them soon, doesn't have to commit to a number up front. They can just say "Give me an offer you think is competitive and I'll consider it in the light of my other options".