Any worthy .org's name will be domain-squatted on the other good TLDs, so they couldn't move it over.
Changing the domain of a site is very effective at killing a site, and a business or organisation, because all existing links to it break, emails to it break.
And if you give up the domain, it will usually get squatted quickly, so the links and emails carry on working - they just go to the squatter's site instead.
There is no way to update the majority of links to your site, if it's been around for a while. You can search for links and ask other site operaters to update, but it just doesn't happen much, and it's also extremely expensive to do when measured in time to write to thousands of site operators individually.
And when you have to change the name at the same time (because your name is squatted on other TLDs), you're effectively deleting the name recognition, literature, old podcasts, matching name you already have on Twitter, etc.
If you had a good name for a long time, chances are you will struggle to find another one like it, and even if you do, most people will think the new name is something else.
On top of that, your email is probably linked to your .org, and people aren't going to stop sending to that for years, no matter how much you tell people to via other channels. You can't know everywhere your email address and main web address are being kept by someone to use later.
And wherever there is a long-standing email domain, there are probably thousands of internet accounts that have that email as their primary or backup/recovery, which you will need to keep if you don't want to start losing access to other accounts. Updating those is very difficult unless you have been extremely diligent at keeping a database of every account you ever created. In practice, even very diligent organisations who attempt to do this don't succeed because accounts tend to be created bydifferent people.
Perhaps in extreme startup land where people start a new business from scratch every couple of years, and pay a lot in SaaS costs so hiked domain fees may sseem relatively cheap, this might not seem to matter.
But many .orgs have been around for decades, and are low budget but very well esablished.
Any many other .orgs are individuals, with email and thousands of online accounts linked to their domain.
There is no "just" to a domain name change.