It has the effect of helping determine how serious the injury/illness is - if they can stop wailing, it's generally not that bad - which gives you time to check out and deal with any injury without getting a headache and if they are still shrieking, despite somebody not showing shock, horror and dismay, there's a good chance that there is something that needs greater examination. (And if they're very, very quiet - too quiet - that gives you a clue that it could be something serious).
Dealing with a lot of children, you get to know the ones who scream blue murder for a broken fingernail and those who barely whimper for a broken finger - sometimes, it's more the shock of something hurting briefly, sometimes (haven't you seen the kid who falls over, is absolutely fine and then they see their Mum's reaction or a speck of blood and start howling?) it's the reaction of the people around them that determines how they act.
The last thing any child needs (or adult, for that matter) is for the person looking after them to be visibly horrified - calm, authoritative and not alarmed is far more reassuring. Just think, what do you think would make somebody with a nasty cut calmer 'Oh, dear, what happened? Lets get you sorted out' or 'OH MY GOD, OH MY GOD, YOU POOR THING, THAT'S AWFUL, QUICK CALL AN AMBULANCE!!! CALL MUMMY!!!'