I want to comment on Jagex's relationship with PKing; from an RS3 growth perspective, not necessarily from an OSRS perspective.
Back in the golden era of RS2, I was in a PKing clan: the most dominant F2P PKing clan at the time, Dark Slayers. DS was undefeated in F2P at the highest levels for over a year. You can still find videos of our run-ins on YouTube.
Here's one of the DS clan sigs from back in the day that highlighted DS's accomplishments:

And here's another that people used:

DS also did limited P2P PKing, but we were mostly F2P.
After DS closed in 2007, I spent a year skilling, then went to college. I essentially stopped PKing. It wasn't just a personal decision. Jagex had removed the Wilderness, removed free trade, and gave us Bounty Hunter, which I loathed. PKing eventually tapered off for me, and I stopped completely.
I had recently argued that Jagex should gamify and reward PKing on RS3, even if it's a minor adjustment, like designating one area of the Wilderness for PKing or building it into a minigame. This would be a start at bringing PKing communities back.
Jagex has never really understood that PKing; or that joining a PKing clan was, for many, the endgame of that era's RS. It has never given weight to the community, even when the community was very vocal, such as Robtokill's "clan support" push in 2006. Here's a pic of Rob and many PKers crashing a secret mod event in 2006:

While Jagex has historically shown antipathy towards PKing, Jagex has understood very well that people are addicted to RS and have their foot in the door, and really no matter what happens, people won't leave.
And in 2006 this might have been reasonable because it is likely that most people based on raw numbers who were playing at that time were either bots or not affiliated with clans. Even after the Wilderness removal and free trade restrictions, people didn't abandon the game en masse until EoC, and that was six years between the two, essentially proving Jagex correct that people would stay no matter the disruption.
I recently heard Asmongold say that PKing is the most difficult thing to successfully balance in an MMO, and that's why devs hate it. He also mentioned that if devs add PvP, it should be unbalanced.
I don't think he's wrong.
This ties into a point I recently made: RS has always been about who was there the longest, who could spend the most time, and exploits. The game has rarely been about true mechanical skill, the kind you see in games like Marvel Rivals, although it does exist, especially with PKing.
So, as a "sandbox," without PKing and minigames, those who seek high mechanical skill activities (outside of PVM) have no outlet on RS3 and migrate to OSRS. In fact, the PKing community on OSRS is still quite large and popular, although according to Framed, it's dying also.
I do think that RS3 can distinguish itself with minigames and PKing-specific areas, but it has to be unbalanced.
A friend of mine, the first F2P player to 126 combat and likely one of the first 100 people who ever signed up for RuneScape, told me what made him rich and when he had the most fun was the transition from Classic to RS2, because so many noobs were in the Wilderness and they didn't know the "glitched" levels like 94 Ranged.
I don't recall the Attack/Strength and Magic levels, but there were levels for each that were more accurate or hit harder than they should have. And players who had been on the game for years would take advantage of that by capping themselves at that level to PK.
So from what I've heard and experience with PKing personally, I believe for PKing to be successful it will need to be something that people can use their experience and skill to create massive disadvantages for others, where high-level rewards are at stake.
I don't know how Jagex does this. I'm not a game developer. But I do know that it would attract interest.
I mostly agree with Framed's historical recap, although I added some commentary below. I also don't think his solutions will work because for PKing to be fun in a game like RS, it should be imbalanced. While I do think PKing should be part of RS, teaching PVP likely still won't get people PVPing.
2:52 - No one called Greater Demons (GDs) "Annakarl" back in the day. Maybe they do now? DS referred to it as "Gladz Castle." Mostly GDs or Greater Demons. Ancient Magicks were released in 2005, which is where the teleport name comes from.
3:03 - People did PK on W18, which eventually became a PK world later, but originally it was just like every other world, but with a bunch of pures at Edge in the Wild.
Clans would world hop in the deep Wild on F2P, usually with "official" or planned run-ins, unless a clan accidentally crossed paths, which became rarer as clans like DI and DS became more dominant.

The video from Bibbleboy is from a P2P war, which wasn't the most common clan PKing at that time. Mostly because multi sucked. A single noob with barrage and no gear could grief your run-in. A lot of noobs could do even worse. Most high-level P2P PKing was in single combat at the Mage Bank or W18 Edgeville.
4:56 - People absolutely knew about tick eating/potting at that time. This is a common myth that we didn't know about ticks in 2006. Combo foods? Most serious PKers on P2P used tuna potatoes, brews (after release), and fell back on sharks.

5:04 - There were established metas. You already mentioned one: no honor PKing (NH). But look at the gear in your own videos, the locations. Those are all metas. You're interpreting the scene from the PoV of an eleven year old, not how it was at that time.
And that happens a few times in an otherwise good video.
6:28 - Why did so many quit after EoC?