Why does Apple Push Notification Service (APNs) use Cellular/Mobile Data over Wi-Fi

Just a guess, but I would say that it has to do with the Wi-Fi going to sleep when the phone goes to sleep. In other words, since the Wi-Fi connection is not maintained when the device is in sleep mode, to receive the push notification, you need to get it via cellular. That wakes up the phone, and causing it to reconnect to Wi-Fi, and would enable you to receive the rest of the message or other data.

WiFi on an iPhone always turns off 30 seconds after the phone goes to sleep. It has nothing to do with the battery state of charge. The reason is that the WiFi protocol uses power continuously, whether data are being transferred or not, so if it stayed on it would run down the battery.

As Lawrence says, and I stated in my post, your Wi-Fi does not stay connected. It turns off as a battery saving measure, but connects again as I stated earlier. As much as you may think it stays connected, it powers down until you wake up the phone. If you are looking after waking it up, that is why you see the Wi-Fi fan.

• Go to Settings/WiFi and note the IP address of the iPhone
• Open a Terminal window on your computer and enter "ping <phone's IP address>"
• Put the phone to sleep
• After approximately 30 seconds the one second ping responses will start to time out
• Wake the phone and the responses will resume

Do the same test and you will see that WiFi still goes off after 30 seconds. Why would the phone decide to block WiFi? It doesn't make any sense.

Anyway, you can test it another way. While the phone is asleep with WiFi on and cellular data off send an email to a Push account and see if you get a notification.

APN is a standard acronym for Access Point Name, not Apple Push.

Plug the phone in if you want push notifications on wifi.
Otherwise turn the notifications off, they only use about 15MB each month, so its not a significant data impact...

Here's the access log of my iPhone, it doesn't block traffic, it disconnects from the AP.

They are not displaying connectivity. They are displaying devices that have leases on an IP address.

Look, this has been discussed ad infinitum for over 7 years in these very forums. WiFi turns off when the phone goes to sleep. That is a fact. Your wanting it to be different will not change that. Your imagining that it is different will not change that.

There's no point in continuing this discussion.