And before you hardwire a power button, as far as making it "always on", you should
test the theory first.
Press and
HOLD the power button while it boots up and make sure it doesn't hang, restart, or just wig out in any way. (this would simulate the button being harwired "on")
If that all goes well, then just tie the two wires from the original button together and it will come on when the powerstrip is turned on.
Different motherboards have a tendancy to do different things.

The older "click-on / click-off" switches were easy to bypass and didn't affect anything else.
But the newer stuff is a different story.
As for just
relocating a button as shown above...... simple enough also.