I'm hoping this exists. I know there are mods that change the attractiveness for certain objects, like bars and espresso machines, so I'm hoping this is something someone else has thought of as well.

I'm looking for a mod, like something I could place on a community lot, that would push Sims to initiate different interactions, such as Dance Together, Classic Dance, Play Catch, Toss Football, Kicky Bag.

I'd like to create community lots where the visitors engage in appropriate activities. A fancy restaurant where Sims Classic Dance after dinner. A gym or park where Sims Play Catch.

I'm thinking it would be an object where these things can be switched on and off, like how there are visitor objects where you can switch on and off which visitors are welcome on a lot.

Has anyone seen anything like this?

I know things like this exist because there's an autonomous random self pregnancy thing someone made for a video
I've also seen other custom objects appeal to sims, making them want to use it. but unfortunately, I don't know of anything that specific does what you're asking for, I just know that it's possible.

I like this idea! It would be great to be able to make community lots where sims do appropriate activities. I've wished for a "Hangout Attractor" I could put in the park under the trees, so sims could sit on the ground in the shade and talk in groups.

Such a mod is possible. You have to create the social object and push both people to do it. You'd have to do some checks to make sure they don't interrupt other activities and do it too often.

I think Toss Football and Kicky Bag are already done autonomously. Changing the attractiveness is different. Here they randomly pick the actions when they feel like it. Some of those actions are set to player or family only and are not accessible even with high attractiveness. But this only applies when clicking on the other people. They can go to a social object directly if pushed by a service object.