Unfortunately sound follows the inverse square law as well, and alarms don't wake me up when they are 6 feet away.
Even if you used the maximum band power of 1 watt, that isn't really enough to do anything. At rest your body will produce about 80 Watts of heat energy, which is a much higher frequency than what your phone gives off and hence has much more energy per quanta. Also keep in mind that 1 Watt is going in all directions, at best you cover half the hemisphere and even assuming phone manufacturers aren't optimizing for phones to radiate away because that gives better reception at lower power, you'd be getting half a watt of energy from a device going maximum transmit power. A standard phone will likely give you less than 5mW of energy dosage.
The most that your phone can do is warm up your ear a bit if you put it under your pillow. By an amount that is likely to be not measurable with modern equipment.
And before noting about ionizing radiation; phones aren't high enough frequency or power to really do that at any appreciable level. Only high frequencies are capable of ionizing since it requires an atom receiving a certain amount of energy per quantum, and the energy per quantum is only related to the frequency, not the transmit power.
You also cannot unplug all of your neighbours routers, TVs and other devices.
It is very easy to get paranoid about specific wireless technologies, it is almost impossible nowadays to avoid "electrosmog" or particularly wireless emitters entirely though.
And if you place it on airplane mode and then turn on WiFi (assuming you have WiFi calling), then you both save battery and make radiation insignificant.