The CDC recommends ground beef cooked to 160F, which is well above “rare” temperature (around 130F). So, you’re going against the food safety guidelines. I’d say that introduces risk (though hard to quantify exactly).

https://www.cdc.gov/foodsafety/communication/bbq-iq.html

That same page says steaks should go to 145F which is pretty far into medium and will get you looked at funny in most reputable steakhouses.

So let's go back to: If you don't quantify risk, you're not providing a useful comment. That applies to the CDC too.

Good luck quantifying real world risks. What’s the risk of getting sick from a rare burger? Well, it’s the probability of a bad bacteria being present, then it not being killed by the cooking, and then actually taking root in your body.. good luck getting a number