There is a myth that Wi-Fi and Bluetooth on iOS devices (and other manufacturer's smartphones) drain your battery. As a result, a lot of people turn off Wi-Fi and/or Bluetooth to "save battery life." This is the result of some self-appointed guru in the trade press years ago saying that Wi-Fi and Bluetooth are energy hogs. It isn't true, and there is no reason to turn either off, and several good reasons to leave them on all the time. Some real facts (for iOS, although similar for other manufacturer's devices):
Wi-Fi is off when an iPhone or iPad is asleep, unless plugged in. So turning it off is redundant.
If WiFi is not actively being used it uses no power. Yes, it scans for networks every 15 seconds when the phone is not asleep, but that's just a receiver, and uses no measurable power (less than 1 mw).
When WiFi is connected it uses 30 mw continuously, whether transferring data or not. But mobile data uses from 50 to to 500 mw depending on signal strength when using data or voice, so Wi-Fi is always the better choice if you are actively using the phone.
Bluetooth uses no energy unless it is connected to a device. So there's no point in turning it off. And you are clearly using it when it is connected, so you don't want to turn it off then, either. While it listens for Bluetooth devices, it uses no measurable energy to do so, as with Wi-Fi.
When Bluetooth has an active paired connection to a hands-free device it consumes 2.5 mw. As the battery capacity of an iPhone 8 (not plus) is about 6900 mwh, if Bluetooth was the only thing using power the battery would run down in about 2800 hours, or about 3 months. Some Bluetooth devices require higher power; the most will be 10 mw, but that still means that if your battery life isn't what you think it should be, the problem is not Bluetooth or Wi-Fi.
What are other reasons that some users turn off Wi-Fi?
To protect against hackers: There are no known hacks that use Wi-Fi with iOS devices running current versions of iOS, so this is not a valid reason to turn off Wi-Fi.
To avoid being tracked: There are services that track your location by detecting your Wi-Fi address (MAC address). 3 years ago Apple recognized this as a privacy issue, and they implemented a way to block MAC address tracking. Unless the network is one that the phone is actively connected to, iOS sends a random MAC address when a network "pings" the iOS device. So you can't be tracked through Wi-Fi. You can override this feature by connecting to, say, a mall's or store's "free" Wi-Fi service. So think twice about using "free" Wi-Fi; it isn't really free; you are paying with your privacy.
So you don't get pop-ups asking if you want to join a network: The correct solution is to go to Settings/Wi-Fi and turn off "ask to join networks."
Why should you leave Wi-Fi and Bluetooth on all the time?
First and foremost, there is no reason to turn them off.
Wi-Fi provides assisted GPS (aGPS) for location services. Apple maintains a database of Wi-Fi networks worldwide. So even if you can't receive GPS satellite signals at all your iOS device can know your location. And when you first acquire GPS satellite signals after changing your location Wi-Fi positioning can speed up the process.
If the phone is screen-locked, connected to power and connected to Wi-Fi if you turn on iCloud Backups the iOS device will back up daily, so the most data you can ever lose if your phone is lost, stolen, breaks or crashes is one day's worth. Which is why it's a good idea to plug your device in overnight, every night.
References (You can search for them by name):
Wi-Fi energy consumption: IEEE Standard 802.11
Bluetooth energy consumption: IEEE Standard 802.15
Cellular energy consumption: Cellular Data Handbook
