Really detailed article, Jessica. Lot of good information.
From my personal experience with 3 companies in 15 years, once you put your paper there should be no reason to accept a counter offer. If individuals have to use resignation as the only tool to start the conversation and you did not get any chance before to share your concerns - then, that's pretty much a clue to leave without accepting the counter offer.
I am sure there are different circumstances and I have seen people resigning just to get a counter offer. One of my previous company used to do the exact thing - offer money when people resign. For some reason, I don't like that approach of retaining the people or the people who use resignation to start a discussion.