When Wifi has no internet, my phone will not automatically use cellular data

Wi-Fi Assist won't help you in that situation. Wi-Fi Assist is designed to address weak Wi-Fi signal strength, not a complete lack of internet connection.

The Apple article focuses on Wi-Fi signal strength, not overall internet access. Wi-Fi Assist is a feature on iPhones and iPads that automatically switches your device to cellular data when the Wi-Fi signal weakens, even if there's technically still a Wi-Fi connection. This can be helpful if you're experiencing slow loading times or dropped connections on Wi-Fi.

The key distinction here is internet availability. While you might be connected to a Wi-Fi network, the signal might be so weak that it can't provide a stable internet connection. This is where Wi-Fi Assist comes in. It recognizes the poor Wi-Fi quality and takes over by using your cellular data to maintain your internet connection.

Since Wi-Fi Assist is enabled by default, your device might unknowingly chew through your cellular data allowance if you're frequently in areas with weak Wi-Fi signals. If you primarily rely on Wi-Fi and want to avoid unexpected cellular data usage, you can disable Wi-Fi Assist in your settings.

In short, Wi-Fi Assist prioritizes staying connected to the internet, even if it means switching to cellular data when Wi-Fi becomes unreliable.

Wi-Fi Assist is on by default. If you don't want your iOS device to stay connected to the Internet when you have a poor Wi-Fi connection, you can disable Wi-Fi Assist. Go to Settings > Cellular or Settings > Mobile Data. Then scroll down and tap the slider for Wi-Fi Assist.

About Wi-Fi Assist - Apple Support