Orgs like Team Aikido had a genuine and helpful purpose and it made the game more enjoyable.

i miss RMO and the tricktionary

I agree, the orgs were an awesome part of toribash. I loved the tricktionary when it was around. It was an awesome way to learn new tricks and show off progress, and many of the people were willing to help you make progress. It was an amazing single player community.

I think they pulled the plug on orgs because the game isn't as big as it used to be and wasn't used as much, so I don't think they'll be come back anytime soon unfortunately.

Pretty much all the orgs (including TA) have been long dead before we've removed the board - they really felt like a graveyard back when we were making the decision whether to keep them or not. The only organization that wasn't removed is ORMO but it looks just as dead as everything else was at this point, despite people still actively sharing replays in Discord and replaymaking scene doing pretty well overall.

In which ways do you think forum organizations can still contribute to the community and why can't that be done within the existing clans system?
I'm emphasising forum there because there clearly are new organizations which exist within Discord, yet they don't seem to have any particular need in having a dedicated forum section (other than just for discoverability purposes, I suppose) - or at least that has been my impression so far.

So if I make a clan called TA and add all the TA moves+knowledge to the clan description that's fine?

Why not, we don't have any strict guidelines on what should be in clan descriptions (or official clans' boards) as long as it doesn't break global rules. If you're making a clan that puts focus on playing aikido-like mods, then I don't see why TA knowledge wouldn't be fitting there.