Most DMs will adjust to your AC...

Why do stormtroopers wear that armor? It doesn't stop blasters, bullets, arrows, or lightsabers. It's not like they get into any fist fights where it would stop punches.
- It varies with the source, but generally it's supposed to be a few things:
  The blasters used in the movie era are... Basically unstoppable? They're the pinnacle of weapon tech as far as mass arming is concerned.
  The armour is supposed to protect the stormtrooper against most "lower tech" weapons, think slug throwers, shrapnel from explosions, vibro-swords.
  Light sabers OP.
  You're supposed to be using droideka-style personal shields if you want to tank energy shots.
  Of course, movies don't think about it too hard and just use them as mooks.
  
  I mean, it does also illustrate how the empire's strength lies in numbers and resources, and not in superior skill. There's some evidence that stormtrooper accuracy is a lot better than popular media gives credit for (e.g. "these blast points are far too accurate for sand-people,") and the only reason stormtroopers miss as much as they do in the movies is because they are under Vader's orders not to injure Luke and Leia, which may or may not be true, but the battle on endor shows how susceptible the armor is to guerilla warfare that does, in fact, utilize those lower-tech weapons. I'm sure if the empire cared enough about the efficacy of the armor, they could develop a suit that incorporated shield technology and win battles with a fraction of the troops they use, but again, the suit's primary function is to mark these shock troops as the face of an insurmountably vast empire. I would not be surprised if the poor defensive qualities of the armor are intentional, to foster a strategic message to the empire's enemies that says "we don't care how many you kill, there will always be more."
  
  A mook? What's a mook? You can't call me a mook.
- I'm not an expert on Star Wars lore, but I think it's to dehumanize them and add them to the greater force of the Empire. The Empire doesn't need individuals for its troopers, they need tools and pawns that will follow orders when given.
  And since they're just pawns, typically recruited en masse, why even cash out for good armor when you can just mass produce the bear minimum for dirt cheap? That's my take anyways
  
  Aren't they all clones of Bubba Fet?
- I think the lore is very mixed on it since even though people love the EU it basically meant every author sort of did different things with it. I believe a common thing with the armor is it does stop the blaster rounds but would make the user's incapacitated. Copout I'm aware but we also have to remember that stormtroopers were always meant to be the elite and most dangerous force but due to them going against people with plot armor they couldn't be good at all. So we have a generations of people who sort of internalized that and basically continued the meme that stormtroopers can't hit the broadside of a barn (even though they were pretty effective in 1 the opening scene and 2 with the rebel base).
  
  The movie even makes it pretty clear that the Stormtroopers weren't trying to hit them during the Death Star escape.
  Princess Leia: They let us go. It was the only reason for the ease of our escape.
  Han Solo: Easy? You call that easy?
  Princess Leia: They're tracking us.
- Great sciencey explanation: https://youtu.be/1r69YZ6YlZw?si=I7YN__toAnAE-f-S
  
  Care to summarise for those of us that can't sit through a 10 minute video?
  
  Damn, that's some nice flow.
  
  That guy has the worst presentation.
- Because Stormtroopers are functionally heavily militarized colonial police more focused on enforcing a terror regime than fighting against peer militaries, and the Rebels are more or less the singular exception. Same reason that wearing typical riot body armor IRL is unlikely to keep you from getting fucked up if someone's shooting .308 at you.
- Most soldiers in war are killed from artillery, and especially shrapnel from artillery and other explosives. The armor they wear protects them from that.
  
  Stormtrooper armour doesn't protect against shrapnel either.

As a fellow dm this always makes me so sad so many experiences this.
For them it is their fantasy same as someone playing a wizard could be casting spells. But yet we never see dm running every monster having antimagic field or legendary resistance.
Let them feel good and invincible! Let tanks be tanks!
- It's definitely an issue at high level too. When I was new to the game, my party had a florge cleric with an unbelievably high AC, with the defensive fighting style from a feat and often cast should of faith in himself, I think having an AC around 25
  I was pretty green and running high level monsters, and I remember him ending up being attacked by a solar with a +15 to hit and something in the encounter offering them reliable advantage and I only realised after the fight that it sucked for the high AC character to not just be damaged every hit, but targeted by the thing they've put effort into instead of something like a weak save.
  Edit: If I found myself overlooking this frequently now, because I had too much to juggle. I'd probably talk to the player and give their PC magic armor that lets them either turn any attack that hits (that isn't a crit) into a miss, or use their AC in place of a Dex saving throw roll (practically an auto-success), once per long rest, or perhaps proficiency bonus per long rest uses.
  That's a pretty janky fix but it puts the tools to retain balance in their hands, and even if it's slapping a bandaid on it, my entire DM style is Dr Frankenstein building bodies with bandaids and kisses.
- Shoot your monks

Oh, the DM will adjust alright.
Me: Paladin with +1 plate armor and shield, AC21. I get dropped at least once per session
DM's wife: barbarian constantly attacking reckless AC17. Never gets hit.
- Don't worry. You may not witness it, but he's fo sho hittin that.

That's just a shitty dm. No dnd is better than bad dnd

So this dm never heard of saving throw attacks?

Nah, it's more fun to let them enjoy their high AC against martial threats but bring in more casters, demons made of poison gas, etc if things are getting too easy.

13AC Abjuration Wizard tanking the same attacks: Pathetic

That's an issue inherent to the d20 system, although 5e is way worse about it. WoD and CoD have way better systems for this, even though they aren't about combat.

Let's say you have 20AC vs this monster +13. The monster hit on 7+. So you have 30% to avoid a hit. This means on average you'll avoid 1 or 2 out of the 5 attacks of the big baddy. Which can definitely save your life!

Or could just use monsters that target players' weakest saves.

And by high AC they mean plate and a shield, for everyone else there's usually no need for the DM to select for high to-hit bonus as enemy to-hit scales up much more than player AC