You're still missing a chore part of the point. In most/all of the world today and in history, when you make something new, your reward is dependent on stopping other people making or selling the same thing without paying you. It therefore makes sense to keep things secret. People don't even always do that, though - if you look at GitHub or Thingiverse, you'll see loads of people giving the right to use their intellectual property away for free. Reasons for that vary, but some are similar to how people would theoretically think under anarcho-communism. Some examples include:

you're annoyed that the previous best way to do something is crap, so you make a new one. The more people copying your design, the less the annoying old one gets used, and the less annoyed you are.
working on interesting projects is interesting in and of itself and finishing annoying ones is satisfying, so when you don't need a particular reward beyond that, there's no reason not to share.
you think your cool new thing will be even cooler if other people collaborate with you, and that's easier if everyone shares their improvements.

As for things that aren't generating intellectual property, and just involve doing labour, the idea is that there'll be enough people upset by something not getting done that they'll do it proactively. E.g. some people will want to take a look at the sewers once a week to check for blockages because they're worried their drains might overflow of they don't. It's not too different to people volunteering to clean up community spaces today, except people wouldn't have to do it on topa of a day job. If that gets too annoying, people will invent new tools to make it easier or totally automate it, whereas they'd have instead been inventing whatever their manager thought would please investors under the current system.

A cultural shift where nearly everyone agreed this was a good way to do things would be necessary, but it's not like they're aren't examples of the same ideas working in the real world.