> I’ve found women are eager to set up a meeting within the first five or so messages, sometimes even hinting at it by the 2nd message
That's probably because they've had enough experience to become aware of "the great lie" with all of these approaches to dating, and are tired of wasting time with it. That is, the fantasy that the online conversation actually has any real meaning whatsoever.
No matter how much time you spend chatting or exchanging messages virtually, it is completely and utterly meaningless when held up against the first 5 minutes of that first in-person meet-up. So getting to that stage as quickly as possible tends to be the best for everyone.