i think that the difference between the tensions may cause it to bend or so ..
If you do it for a while, like a year or so non stop, maybe the neck will tinge a tiny bit, but then thats just a matter of truss rod adjustments, if it has happened, just go to your closest store and they'll figure out how much to adjust the truss rod if you don't know.

But still, not likely if you just tune between C and D and standard E
Gear: Warmoth Soloist / Hondo Acou. / Ibanez AS73

Hardwire TL-2 / Boss GE-7 / Electro Harmonix Small Stone Nano / Boss DD-3 / MXR Smart Gate / Ibanez TS9 / Unknown Tremolo

Bugera V55 / Home Made Cab w/ Celestion Speakers G12M & G12T
it will definatly ruin the strings after a time but the neck should be fine.. (best double check though )
Who decided that pie would be sold on Tuesday but not Wednesday?
the only problem will most likely be having to adjust ur truss rod and basically just doing a set up.
Could that also mess with the nut if you do it daily? Not to where the strings get super floppy, but make the slot a bit bigger.
only if ur using different string gauges, but either way if u dont know what ur doing dont try to file the nut, take it to someone who knows what theyre doing