Honestly I woke up a very short while ago, and am pretty busy, so this might be shorter than it would otherwise be. But I hope my points are understandable.
Ultimately the disagreement here is you want Evangelion to become CONTENT.
I want it to stay an expression of an artists emotions while telling a STORY.
Honestly I'm not sure what you want to say with this. I don't want some of the concepts of Eva, and the potential discussion its impact and popularity would lead to to go to waste, but I still want stories. You mention later in the post that there has been Evangelion content for years, and yes, that's where I might draw a distinction. We've had games and manga with very specific audiences and fanservicey goals, stories that are trapped in a certain ecosystem and that couldn't go outside certain limits.
When I say I want more Eva stories (which Anno dooes too), I want truly free artists who
want to work with Eva to tell their story. Artists going back to previously existing great art to explore new ideas isn't rare, here it's just actually possible despite copyright still being an issue. In some cases that leads to work superior than the original.
I want the artists, having told their story in this world, to end their story and continue on to new and original works. To tell stories in worlds we don't know we want until they show them to us.
That is entirely possible within the Evangelion franchise IMO, and this:
You want the artists, having told their story in this world, restrain their creativity and find new ways to keep the same story going forward. You want the same story and world just with a slightly newer coat of paint.
is precisely what I don't want, something more similar to what we've had till now in spin offs, and something most likely Anno wouldn't even let past the concept phase in his position as supervisor/director of khara.
This argument will be 100 times more valid and depressing if Khara uses their finite resources in the future to making Evangelion Prequels, Evangelion Sequels and Evangelion Spin-Offs
I really doubt anything set in the same world would ever come to fruition. I don't want that either but I don't think it's something we have to worry about under Anno's khara.
Honestly to me Anno's Eva ending and probably future works not focusing on Shinji and co. already means Eva having the self-control to end" is an oxymoron that literally contradicts itself every other word and means nothing.
It means anything new might be completely unrecognizable to us. Evangelion currently means "Anno's vision", it's what we know and have known for years. We most likely can't even imagine what might be made in the future using some of Eva's elements.
It's a given if Khara made a sequel set 30 years after the Rebuilds end the number one debate will be whether or not the main character is Shinji's child and if yes then who is the mother? Who did Shinji end up? What's Shinji's story?
I think you're kinda underselling khara's creativity here. Even that Neon Genesis Impacta short from Animator Expo did none of that despite actually being set in the world of Rebuild.
If you're making a film or TV series in the Star Wars universe an artist can do whatever they want... as long as they don't stray too far from what was done 30 years ago and what fans want. In fact, just make it cool
I don't think we should compare Disney-owned Lucasfilm to khara, but even they somehow allowed Last Jedi. I'd just expect greater liberty in the Eva franchise.
I'd rather Khara use its very finite resources to support an artist spearheading a story that is new, original, inspired by Evangelion and free to go and do whatever it wants without having to check a list of boxes for what an Eva thing should do. You want the checklist.
Rather I want an artist to prove such a checklist doesn't exist.
The film had no limits. It had no boundaries. It was free to go and do whatever it wanted and at no point was it shackled by the needs of a franchise
I'd argue that not being able to tell a story within a certain franchise would be a limitation as well to some artists. Maybe their idea requires working within it to maximize reach/impact, maybe they want to contradict all of Eva using the same language, maybe they want to fool us or just genuinely surprise us when we go to watch the next Eva. Maybe they are ready to create a masterpiece and just need khara's approval to create it.
Now I would add that looking at Anno's work you can see the potential of working in franchises.
Kare Kano is a manga adaptation.
Love&Pop and Shiki-Jitsu adapted novels.
Cutie Honey is part of a franchise with who knows how many iterations (in this case he even adapted his own film to anime).
His short film Ryusei Kacho is a manga adaptation.
The Giant God short film he worked on is a Nadia prequel.
His Rebuild is continuing his own Eva franchise.
And IMO the best example: his Shin Godzilla.
Edit: I don't know if Nadia should be on that list, but it does take some elements from 20.000 Leagues Under the Sea.