I disagree, the only power which is unique to God is the ability to change reality without natural means of doing so, therefore we have to know the means by which they perform the change in order to know it is supernatural and not natural.
Otherwise David Copperfield, Sai Baba and numerous other miracle workers could be said to be the trustees of God.
In my opinion.
It's not about the power being unique to God, but would he entrust such power to servants that are deceivers and liars?
The same thing that would show the day of judgment in theory would be a proof for God and his authority and his Prophets and trusted witnesses, shows miracles to be a proof.
This would be like saying on the day of judgment, people will have no reason to believe still and are justified to doubt. It doesn't make sense.