It may depend on which particular visa you’re entering the country on (visa on arrival/ETAs are often more lax or might not have the requirement at all). If you don’t need to apply for a traditional visa in advance (you know, where you have to show up at an embassy with a bunch of paperwork), you may not be required to ever show proof of insurance.
Although countries could also choose to verify insurance details as part of the immigration procedure on arrival, I also haven’t experienced that as someone with a top-tier European passport.
Some examples of countries requiring proof of health insurance coverage here. I personally needed to show proof of insurance when traveling to the US on a J-1 visa (when submitting the visa application).
EDIT: Here are the official requirements for the Schengen visa, including medical insurance coverage of 30,000 EUR minimum.