It’s a legacy restriction - it was just that they banned any radio transmitters, probably originally because older analogue radio transmitters could interfere with the aircraft’s radios and things.

I don’t think there would have ever been any legitimate concern of low-power digital devices like mobile phones causing any problems like coupling into control systems or anything... Digital radios are typically much better filtered and far lower power than analogue radios.

The company I work for makes satellite antennas for ships and large road vehicles, and the only time we’ve had a problem like that was when somebody mounted a 20kW S-band weather radar three metres from our antenna. It just requires a little extra shielding in one module though.

That's an interesting point, although you have to remember airplane mode turns off all radios on the device, not only the Wi-Fi. They probably use it as a "fool-proof" method to prevent any unintentional interference with both current and future wireless devices.

That being said, unofficially I agree, given Wi-Fi is provided on flights now, I'm sure that means you're alright to leave your Wi-Fi radio on. The answer to why shut off all GSM/CDMA, Bluetooth, and GPS radios as well, however, probably predates the high prevalence of all these wireless technologies in a unified device.

There are no FAA regulations regarding phones/electronic devices other than a blanket rule that you can only enable them with the permission of the captain. The rules regarding cellphone use on planes is from the FCC. They don't want tubes full of transceivers broadcasting at max power (phones ramp up power to search for towers where there are none) high above the earth where they can broadcast over the greatest physical area. At 30k+ft this is not a huge concern (too high for a noticeable increase in the noise floor) but in terminal areas they could conceivably tie up bandwidth on every tower in the city. Whether this is a concern with modern cell towers is up for debate however.