My guess is because your battery will die very fast if it kept constant connection to wifi when its not needed.
And that 99% of people that have iphones have data plans so they dont solely rely on wifi to get their notifications.
This is correct, having WiFi on while the phone is asleep will consume more battery. The reason is that the phone will always be running the cellular radio, when the device is awake or asleep the cellular radio is always active, the reason is simple... ITS A PHONE, the purpose of a phone is for phone call/be connected, so the cellular radio has to be on all the
How so?
If your cell tower is not near you and you have 2-3 bars signal, then that can't be better than reception of your router that is 1-2m away. Of course there is drainage if your wifi constantly goes on and off instead that it is always connected.
Bad reception = slower network = delayed notifications
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That periodically is not push and that's why we have delayed notification. If it stayed connected then notifications will come as a push.
Having WiFi on while the phone is asleep will consume more battery. The reason is that the phone will always be running the cellular radio, when the device is awake or asleep the cellular radio is always active. The reason is simple... ITS A PHONE, the purpose of a phone is for phone calls/to be connected, so the cellular radio has to be on all the time by design.
When the device is awake it will run the cellular radio which is always running and turn on the WiFi radio for data. However when the device goes to sleep it'll turn off the WiFi radio to conserve battery power, since it's not needed. By forcing WiFi on while the device is asleep your causing it to run both radios which is consuming more battery power. Also when the device is asleep there isn't much data transfer, so there is no point in running two radios for such minuscule amounts of background traffic.
Remember if the phone is doing something like streaming music from Spotify and you turn off the screen, the phone is still using WiFi. It's only when nothing is actively using WiFi that the phone will turn it off while the screen is off/ phone asleep.