My point was not about whether people are incapable of understanding exponentials, it was about whether they understand them intuitively. You used the term “reflexive response” but what we’re both describing is intuitive or automatic thinking.

Why is it relevant that people don’t correctly apply exponential reasoning automatically? Because when people encounter information in everyday life (outside of the specific job they’ve been trained to do) they tend to use intuitive thinking predominantly. This matters a hell of a lot when it comes to making political decisions of a technical nature, such as infectious disease planning and response. Lo and behold, this is the exact problem the Italians are trying to warn everyone about!

Show someone an animation of the lily pads doubling every day and ask the same question and you’ll realise that they understand exponential growth intuitively, they’re just not good at word problems.

Show someone an animation of the lily pads doubling every day and ask them when the pond is half-covered? You're not even asking them to solve a problem at that point, only to point at the animation when it looks half-covered.

Relating this to the spread of the virus, people aren't carrying around an animation of this in their minds. Perhaps science communicators should do a better job of communication and produce such an animation? But then you're still not getting people to understand the concept. You're telling them "this is what it looks like, sort of, now just trust us." The problem is that people don't trust scientists (and mathematicians) as it is.

Yes, the point being that linear halving is much more intuitive for most people than exponential halving. Even when you're told the doubling rate, your brain reaches for the wrong answer every time.