The result is that the only way for someone who isn't wealthy to do charitable work is to get either Government or companies to pay you to do it. Companies will generally only pay you to do work if they're getting something out of it, and Government has its own interests at heart.
Getting people to pay you to do something is very, very difficult - it's hard enough if you're selling them something directly and right now, significantly harder if you're still working on a project, and harder still if there might not be anything concretely benefiting the person donating at the end of it. Charities largely manage by not paying many of the people who perform work for them, along with begging money from Government and companies, and their volunteers primarily depend on Government welfare.
It's not a perfect system in the slightest - it's incredibly hard work to be able to perform any sort of charitable work, at least as hard as running a business, and is heavily subsidized. A system which ensured that everyone's needs were met by default, rather than requiring you to prove that you deserve to have your needs met, would allow significantly more charitable work - specifically, it would allow for work that rewards the worker in ways other than monetary pay.