I think in this case it's important to clarify what we mean by financial independence. Being able to address emergencies and setbacks is a very different level of wealth than having accumulated enough that you can live only on the interest. I'm not arguing against the former obviously. I'm saying that the latter looks like an arbitrary and somewhat meaningless goal to me personally.

Also, the setbacks that you might experience vary a lot. You gave an example of suddenly becoming disabled - in that case you might find that all of the formulas that you've used to compute that you've reached FI don't work anymore because your expenses have increased dramatically. So you were financially independent before but now suddenly you aren't anymore? Then maybe you were never financially independent in the first place. (There was a great story about this on HN - https://news.ycombinator.com/item?id=26543527)

That's another problem with the whole FI(RE) movement - it pretends to have quantified something that can't be quantified by just making a lot of assumptions about your future needs and wants, the state of the world, the stock market, inflation etc. And when those assumptions are questioned, the defending argument boils down to "having more money is better". Which of course I can't disagree with. Just don't pretend that you've achieved something that you haven't by claiming to be financially independent.