It’s way easier and more reliable to keep track of money in an accounting system than in random tiny pieces of paper. Money is safer in a bank account than as a tiny piece of paper.

In terms of business process, it’s better to have one single standard procedure of depositing (not cashing, ha) every check right away. Rather than asking any person handling a check to go through some sort of decision tree on the spot.

If you need to return the money later you can always cut your own check.