By reading the capture from the Apple website you've just posted there are no such security risk as the one I thought you had just discovered by your post. In the capture it says the watch would only connect to wifi networks if your iPhone has previously connected to them. So there are no out of control wifi connections happening on the Watch. As long as you don't connect your iPhone to risky wifi networks it's fine.
Now, going to the topic of why it is not recommended to connect to public wifi networks. Public wifi networks are such a useful tool for tourists in need of an internet connection. However they should only be used in case of extreme necessity.
The reason is that when you connect your device to a wifi network all the information that goes out of your device to the internet hast to pass through the router. When you are in the middle of street and see an unprotected hotspot you can't make sure that this wifi is trustful as anyone could turn on a wifi hotspot anywhere and name it as they please.
If you connect to a wifi network that's being monitored by some sniffer software they could not only spy all your connections but also perform attacks Man In The Middle, where they would steal all the information you send through the internet unencrypted, and also if they have the right tools they could exploit the vulnerabilities of your software to infect your device an.
These risks are a true thing happening today in the world where there are not just people willing to hack other people's devices, but also organisations that use bot networks to perform this attacks automatically to collect information. I know most of people aren't aware of these dangers and some other just try to ignore them in order to live happier unworried lives. But these things shouldn't be treated as fairy tails as they are real.
Going back to Apple, they have proved to worry so much about security that their products are considered nowadays the most secure platforms among their kind. However they are not flawless and have vulnerabilities just as much as any other platforms. The difference is that Apple tend to fix these flaws as soon as they acknowledge them. These makes Apple products very safe when they are updated. But very safe is not enough as some of these attacks tend to happen outside of the Apple product, like sniffer software or a Man In The Middle attack. So we should never forget about security even when using an updated Apple product.
But in the real world not every tourist have an updated Apple product but an outdated Android product, and they tend to careless connect to any random wifi they cannot verify. These behaviours are quite dangerous and we should all raise awareness about it.