Doing so will open Pandora's metaphorical box.
In order to unlock the phone, Apple would have to write software that was never intended to exist.
Imagine a variety of padlock. Not an ordinary padlock, this one was specially designed to have no master keys. Every lock sold has one key and only one; only the owner of the lock (or holder of the key) can open the lock. The lock even has a self-destruct mechanism so that any attempt to pick it will, on the 10th attempt, utterly obliterate both the lock itself and whatever it had been securing.
Now the government wants the manufacturer to design a master key, one that will defeat the self-destruct mechanism. "Just for the one lock, not for all of the millions that have been sold."
But master keys don't work that way. A master key opens all like locks. If it opens that one lock, it would open them all.
[Note: I am not an Apple fan in any way. To be honest, I don't like any of their stuff at all. I use none of their devices or software. Once upon a time I used QuickTime to view .mov files, but VLC does that without inflicting a foreign interface upon my desktop. I've tried Macs and hate them. I have no smartphone, but if I did, it would be an Android device.]