No, no, no, it's absolutely not the same, OMG, nothing alike. "I dont want to go to the gym today" isn't the kind of profound, all encompassing, and existential dread that attempting to organize a social event is. Especially when you push yourself to organize and it doesn't work out, which has happened to me before. Those feelings are legitimately nothing alike, the fact someone is comparing the two is wild to me.
I do still need to try to overcome it and get over it, but it's not even as remotely as simple as you claim.
When this doesn't happen what do you do?
The only other option is to go on being miserable.
If you feel you're clinically depressed get diagnosed and treated in a clinical setting ASAP. Diseases need treatment.
You generally do not go to the gym and fail, exercising works more or less the same for almost everyone, you get good hormones, you feel good.
Socialising, on the other hand, is entirely different. Some people thrive in it, some people feel much more dread afterwards.
Even if there were state programs that established and ran these sorts of events and created low-friction ways of interacting with people, people could still say "well that assumes a certain baseline of energy."
It is true that somebody who is in the midst of extreme depression and can't get out of bed is probably not going to be able to set up a local dnd game. It is also the case that the large majority of people are absolutely capable of doing this sort of thing.
If I may I made an attempt to crack at this very problem with Tatapp (tatapp.astekita.com). Any feedback is very much appreciated.