This advice does not make much sense, DFU Mode is for performing a full restore on a device. It is not a way you'd just carry a device around, I believe it actually reboots after a certain amount of time.
At that point just walking around with a powered off device makes more sense than DFU.
Maybe this is not an option for you and you prefer turning it off if you want to protect yourself against nation state attackers. I assume the DFU mode ROM is hardcoded and therefore more difficult to attack, but if you have heard of DFU mode attacks/simulations/circumventions, by all means let us know. Turning a device off can be easy simulated on a jailbroken device as Snowden argued by asking journalist to put their devices in the fridge.
I wasn't aware that an iDevice comes out of DFU mode after some time, please enlighten us. According to the instructions [0] I understand you need a special set of actions to return to the normal firmware.
I am curious where your thoughts on DFU come from. I am very familiar with it as it was the bootrom-level recovery mode my team utilized when we worked on jailbreak tools that exploited SecureROM.
DFU has a single purpose: wait for an Apple-signed firmware file to be sent to it over USB for it to execute. You seem to indicate that it's something you would carry your phone around in...in which it would just reboot into iOS after awhile.
Asking the obvious: Have you booted an iOS device into DFU mode before? Maybe the iPhone Wiki made it sound like it is a "mode" you can boot iOS into? I am not sure exactly what you think it is, but again, the device screen is completely black and indistinguishable from being off, OS is not booted and nothing is happening at all, besides the fact that (again) it is indeed on and "spinning" as it waits for the USB interrupt.
Excellent idea, similar to what Snowden used three years ago with a fridge. Don't forget to turn off your device or put it in airplane mode because you batteries will run down quickly as it will try to find a GSM transmitter. Unless of course you're device is used as a surveillance device and transmitting even if seemingly off/in-airplane-mode....
There are many options and as always in security/warfare/sports/etc the best defense depends on the attacker, the circumstances, the capabilities of the defender etc. DFU mode probably is one more option in a list of options and it has the advantage that it is available most of the times (it has to be practiced as always in security/warfare/sports/etc) and, for now, probably not hacked. If Will Strafach shows us that an iDevice reboots out of DFU mode after some time, that is one more thing to take in consideration. Or if it is not possible to carry an iDevice around in DFU mode, it might be useful only in limited cases.
Again, there is zero use in an iOS device being carried in DFU mode. All that will do is waste battery, because the single function of DFU mode is to wait for the USB interrupt started by a computer sending a Apple-signed bootloader to use to boostrap loading of the firmware restore RAM disk.
As previously mentioned, it seems that you have the idea that DFU is a "mode" that you can boot iOS into. This is absolutely not the case, the device screen is completely black and the device appears to be completely off, because it almost is, it's just "spinning" and waiting for the USB interrupt.
The reason I am very adamant about this is because your comment was upvoted when the advice would serve no purpose to someone who needed it.
If you do not believe the device will reboot, go get an iPhone now and boot into DFU mode while plugged in. Then look at your computer and wait for it to recognize the DFU connected device (only way to know when it's in DFU versus being off). Then unplug it and watch, it will reboot into normal iOS at some point (or power itself off if battery is low, depends, same point though).
At that point just walking around with a powered off device makes more sense than DFU.