IPad – how to turn on empty iPad while loading

Like you said in a comment, it's more a software limitation. Even though there's probably some hardware safeguard.

If you plug your iPhone a millisecond before it reaches the shutdown limit, then, no harm done, it doesn't need to shut down, power is there to keep the phone running and recharge the battery.

If you plug you phone after the shutdown limit, then the limitation is in place to ensure things will go well the next time you power it up. If it allowed to power up the phone any time, then what if it is unplugged while booting. There wouldn't be enough juice for the phone to be fully back on and it would shutdown while booting.

That's something that could damage the phone or the OS.

So to ensure that this wouldn't happen, Apple probably put the arbitrary 5% limit.

If you are not near an Apple store or Authorised Service Provider then call up AppleCare (apple.com/contact) and they will help you try a few steps and if they come to the conclusion that your iPad needs to be swapped then they will send you one. Pretty sweet deal. I encourage purchasing AppleCare+ as well while you talk to the phone agent because you have a small period of time to purchase it and it is a fantastic investment.