Well, actually what you're implying would have to involve magic. If you removed your phone's battery and then expected your phone to be able to start itself up that would be matter of defying laws of physics.
https://en.wikipedia.org/wiki/Scientific_law
When you press the Power button on your phone, it's not an actual, physical switch where you connect/break a connection between the battery and the logic board, it's simply sending an electronic signal to either boot up or down. And those electronic signals can only exist when there's at least some power. It's not unlike a DVR player in your entertainment center where there's a little display showing the time, and you can use a remote to turn it on or off. The switch on that player is not an actual, physical switch either. If it was, the always-visible time display or the ability to detect the infra-red remote signal would also require magic. In that case the switch is just sending out signals for the player to do different functions. As for PCs that can be set to turn on/off in the BIOS or UEFI, PCs have CMOS batteries that retain things like time and hardware config settings even if the power cord is removed, smartphones do not. They rely solely upon the main battery (well, for some semi-permanent hardware config data a programmable firmware chip but that doesn't involve user data retention.)
Anyway, your phone does require at least some power at all times even when it's 'powered off'. That's essentially just nit-picking something that typically doesn't matter, but in this particular instance you do need to be aware of what's involved to do what you want. I'd suggest just enabling Airport Mode at night and letting your phone go into its low-power, deep sleep mode but whatever.