"Drums. Drums in the deep."

I miss a time when orcs had axes, not feelings.

The party pursued the group of orcs as they withdrew from the fight.  After a time, a war horn sounded from the rear, followed by horns to either side.  Suddenly the party began to look for a place to make a stand.  As it turned out, it would be their final stand.

I ran orcs how I imagined a street or biker gang would operate. They had territories, wore their 'colors' with pride, had affiliations and conflicts with other ork tribes, demand payment from weaker groups operating in their territory (bandits, kobolds, low level adventuring parties etc.) and would hire out as mercenaries to someone to powerful to reasonable defeat (watch your back around them if you're weakened somehow. And keep a close eye out if you hire bands from different tribes that have a 'beef' with each other). There were usually between 80 and 100 (100-d20 ignore a 1) orks per tribe in war bands of 3-12 (d10+2) available as mercs.

There’s a reason there’s always a bunch of half orcs in town

Orcs featured in most of my campaigns, and not only at low level. As you stated, they are organized, intelligent, and capable of conquest. In my main campaign back in high school, an orc war chief declared war on a neighboring kingdom after adventurers from that kingdom raided one of his orc outposts and massacred dozens of his warriors. The resulting conflict was epic, and my players learned to fear orcs after that, regardless of their PC's level. One PC almost lost his castle and lands during the conflict (I've always used dominion play in my games when players reach name level).

I miss the classic orc.  Snarling, nasty, and chaotic.  Smart enough to be a problem.

I've played in some campaigns where one of the orcs in a group would run away in every encounter so that a group would hunt us constantly, making it hard to get the rest spellcasters needed.

"Nobody tells stories about fighting three balanced enemies in a finely tuned encounter".

By Crom, as a D&D player who got his first manual in 1987, I needed that so much words can't even begin to express the magnitude.

Thanks for using the pig-headed orc for your art. I miss them so and feel it was a mistake to lose this in later editions.

Years ago I took out a group of 5th lvl PC’s with 24 goblins, a couple of wolves and terrain management

I played and DMed quite a bit in my time. As a player, I always liked to set traps for the monsters. I always carried oil, spikes, rope, etc.. and I used them a lot to create triplines and flaming hazards for the enemy. I loved taking the rope trick spell as a mage. Most of the other players would look at me and ask why rope trick and not Melfs acid arrow. I would just shrug and show them when we were in a nasty situation in the dungeon. I saved an entire party from drowning in a water pit trap by opening my rope trick up and waiting for the trap to drain and reset. I saved several entire parties that way in a multitude of situations. You never know what uses you can get out of something until you try it. It does not matter the hit dice and power level of the opponent on paper, it is what they are potentially capable of in a variety of situations as you indicated. D&D used to be about thinking outside the box and critical thinking in difficult situations. Now it is all soft and fluffy fairy dragon BS.

Organized enemies like orcs, kobolds, goblins, hobgoblins and such were nightmares for my parties when I DMed regardless of their levels. Orcs made for great running campaigns well into mid-level and above since regular orcs were still meat shields for their leaders. At higher level, the characters were getting past the regular troops and meeting the big boss, who was not some measly peon.. but a magic item weilding shaman that had used his intelligence and strength to mold several hundred orcs into a force that challenged the players through their entire careers and the regions around for a decade.

I've seen illustrations from the very first editions of D&D featuring orcs with porcine faces, which is much less in keeping with today's idea of ​​orcs (heavily influenced by the Lotr film trilogy). This early depiction of orcs in mainstream fantasy (between the 1970s and 1990s) could explain why orcs (and similar creatures) have porcine features in many Japanese works.

This is why i maintain that a first- or second-level adventure should be mostly traps and puzzles with a few giant rats, large spiders, rust monsters, and oozes.

In old school Basic/Expert/AD&D, Orcs and their kin (Goblins, Gnolls, Kobalds, Flinds, etc.) were something you best avoid if possible. And usually, they were in the service of someone, or something, even worse it was best not to draw the attention of.

They had trade systems fir tithes, artillery crews. They were awesome in AD&D

In 2e an orc was roughly rquivelent to a level 1 fighter

Whenever I play as the evil wizard in Heroquest I like to play the monsters differently based on what they are. Creatures like Goblins and Zombies I play as mindless aggressors; they attack whoever is closest, no matter what, and never retreat. Things like Orcs and Bandits I play as being on par with basic adventurers; they will attack whoever makes the most sense to, retreat to better positions, and use other basic battle tactics. Really powerful enemies, like Gargoyles or Spellcasters, I will roll dice to decide their actions ( even number = attack, odd number = spell, then roll again to decide who gets targeted ).
Sometimes I will have one "intelligent" Goblin in a group that I will play like I would an Orc, like a little leader for the group.

Add class levels to anything and it gets scary real quick.

Running a group of new players through good old Keep on the Borderlands. They're soon to meet the terror that is the orc cave. It's Shadowdark, so they might stand more of a chance in combat, but it won't be pretty at all if they charge in.