I think often times it is the terms that we use that gets in the way of explaining or understanding. Unfortunately, I say parry, you say block (or visa versa) and are meanings get mixed.
For example, in a boxing match, you would rarely (if ever) see a boxer use a box/parry (in for example the karate termonology). The closest thing a boxer uses to a parry (other that just putting his arms up to let the opponet hit his forearms) or would be another punch. You don't really see parrying in boxing. i hope I am not mixing my terms too much. Basically, humans are rarely fast enough to parry a real in-coming punch. Oh, in the dojo, we are plenty fast-- often because the punch is at half speed. But not usually in real life. Now that is not to say, I am against side-stepping or moving. But to parry, parry, parry, seems to be a losing proposition.
You insist on starting from a bad premise, namely that parries don't work. And you're assuming that boxing is an adequate representation of a real fight... (That's a whole 'nother thread!)
Research boxing a little... You'll find that there are actually blocks and parries in boxing. They don't stand out for several reasons (very restricted targets involved, movement that accompanies them, lack of appreciation for counterfighting currently, are just a few of them) -- but they are there.
You're assuming that people aren't fast enough to parry an incoming punch. Someone must have been -- or the techniques wouldn't exist in martial training.
I suspect that part of your problem is some common poor training habits. Very few people ever really learn to work properly with a partner; they learn to pound a bag, they learn to "spar" or "rock-n-roll" or "thump", they learn kata or shadowboxing... But they never learn to work WITH a partner to develop a technique. I'll use a simple outward parry, since that's the topic, to explain. I think most of us can picture fighting left foot forward, and using the lead (left) hand in an outward/counter-clockwise circle to contact and redirect a right hand punch from our partner, then following up with a right hand punch. (Choose your own footwork -- but use some!) How do we go about learning this?
First, practice the motions in the air, no opponent. Figure out your balance, where your hands need to be, how deep you think you need to step and so on. (This is just kata training or shadowboxing in disguise.) Then... grab your partner. Set up at a REALISTIC range (this is vital!), and assign your roles. (He's punching, your parrying.)
The first few times -- your partner's throwing the punch easy, maybe half speed or less, with plenty of warning, maybe even on a command. You're shifting it off effortlessly because he's not making it hard for you. You ARE finding out how you have to step around him, about when you have to move to parry the hand and be in position to strike, and so on. One catch... YOU can't go full speed when your partner's going half speed. Y'gotta both play at the same pace!
After a bit (how long depends on your skill and how fast you're picking things up) -- your partner starts to pick up the speed and intensity. Now it's not so easy to move him and he's not giving you as much notice. It's getting trickier... but stick with it. Don't cheat the technique, and keep your speeds the same. With more practice, pick up the speed even more.
Finally, your partner is going almost full speed (or even full speed if your skill levels are there), no notice, and even varying the attack or the target he's punching at. And you're going just as fast... I bet you find out that you can parry a strike.
Lots of people are lousy partners; they don't throw good strikes or they make it too easy (or too hard!) for the person they're training with. They move at full speed when attacked at half, or they move at half when attacked at full. If you're feeding the technique, your job is to throw a good, effective strike that your partner MUST block/parry/trap or otherwise respond correctly to, or they get hit. (With good control, they shouldn't usually be hurt, though it remains a possibility.) If you're practicing the technique -- your job is to do THAT technique, not something else, not something that "works" or "feels right" and to match your partner's speed.