Not everyone’s opportunities are the same. If you can afford to be pushy and can afford to walk away, then sure - do that. However, I personally would not put the whole opportunity on the line and walk away just because a recruiter won’t tell me a range. In my last interview they didn’t give me any range, while I gave them my expectation, which was a bit inflated, and they just accepted my offer. Could I get more if I knew the range? Probably. But I can’t be mad at them, as they matched my expectation. And I enjoy the job so far.

It all depends on the situation, as you also mentioned. I’m just arguing that saying “walk away if they don’t tell you a range” is a bit of an exagge and might do more harm to some people than good.