Being self-sufficient should be a goal for every human being to strive for. Independence is a potent form of freedom that makes you feel like a magical eagle.
I'm not saying you should be Ted Kazynski or however you spell the Unabomber's last name and live in complete isolation for most of your life, because it's cool to have access to society's benefits and all. But the more you can do for yourself, the more secure you will be in all ways. Basically don't be a helpless or useless person.
The more self-sufficient you can be, the fewer societal resources you will take up, which could then go to someone else in greater need. That's my perspective at least.
The organization I work for is all about helping people get back on their feet, and while I would never want to tell someone they should be more self-sufficient and rely less on us, there's no denying that our resources are already stretched thin. At times, it forces us to prioritize those with the greatest need, even when others still need help.
The more self-sufficient you can be, the fewer societal resources you will take up, which could then go to someone else in greater need. That's my perspective at least.
But the more self-sufficient you are, the more resources of yourself you need to supply yourself. So you can provide less societal resources. If you do not need to provide clothes for yourself, you have more time caring for elderly, etc.
As another view, the total resources need does not directly change by changing who does what. The advantages of helping each other are in the OP. At some point however, I would think, the overhead of organization grows so large that it may not be worth it anymore. Just think of the amount of work put into "useless" administration in many countries. But in a 30 person village, this is probably negligible.
Edit: Thanks for helping other people on the feet!
That is a good point, but I would consider resources needed to maintain stability versus resources needed to achieve stability. Metaphorically, it's easy to stand on top of a mountain, but it's a lot harder to climb it from the bottom. And the mountain gets taller the longer you wait.
Once you're at the top, you can lend a hand to the people still making the climb without worrying about being pulled back down.
How would one get in touch with such an organization should they find themselves off their feet unexpectedly?
Not having any issues right now, but I think it might be easier to get an idea now that I have resources like a phone with access to the internet than after finding myself in such a position where who knows if I'll own anything.
Out of risk of doxxing myself, I don't want to give too much information, but specifically we work to help set up immigrants and refugees with housing, healthcare, education, and other resources, so I am not sure if it necessarily applies to your circumstances. Though my particular role is not that glamorous, I just maintain the infrastructure.
If you're in the US, you can often dial 211 (depending on your city) to get connected with various resources depending on need, or crisis lifelines in an emergency. Local and state governments will also often host sites or portals with access to various social services they offer. Sometimes even a 211 website for both at once.
In emergencies, hospitals will also always be able to help, but keep in mind a lot of their services are not free. Ask up front if various consults/appointments come with a charge before you end up with a bill. But even if they're unable to provide anything directly without charge, they can often still put you in contact with services they contract with, such as social workers or community wellness representatives, who may be able to provide free help depending on your circumstances.
I've heard even just popping over to public institutions like town hall or the local library (but not schools, avoid schools if you look homeless) can be a helpful place to start to get familiar with resources in the community.