There is plenty of reason to wait until morning if your talking about a bow shot that was forward.
Maybe. In my opinion there is also plenty of reason to go back to camp get a cup of coffee some warm food in your belly get a flash light and come back in an hour. No reason to let it sit 12 hours when 1 would do the trick.
There are certain shots that I always wait until morning. I actually prefer to track at night, can locate blood better.
If the shot was forward, it is iffy on the recovery depending on the elevation. If he could see the arrow sticking out, it more than likely buried in one of the shoulders.
Front shot or high shot take longer for the blood to start dripping and actually reaching the ground. It can make tracking difficult. I have seen some make it 40-50 yards before finding any sign.
I shot a doe this weekend in the shoulder and she made it about 30 yards before flipping head over heels and piling up. My father shot a spike in the shoulder and we tracked it 400 yards and ended up bumping him the next morning. If he had giving him until the morning, might have stowed up enough and stayed put.
As a hunter, you have to make the decision that you think is best for the animal and possible recovery. I dread bumping an animal after it has laid up. Typically the blood trail is virtually non-existing after being bumped and if you let them lay long enough, many times they are to weak to make it back up and if they do, they cant make it as far.