Let me ask you this: do you think the money system does away with thieves, mooches, the lazy & the greedy? Have you considered that thieves & mooches & lazy & greedy people might just be a product of the money system?
The greatest thieves and mooches and lazy and greedy people are at the top of the money system: bankers and stock brokers and CEOs, who not only contribute little or nothing to society, but bleed the goods from the workers at the bottom. The very pattern of money society since ancient Sumer & Egypt has been for wealth to flow from the workers to the non-workers, from the industrious to the lazy. When you take more than you need, you are a thief. The very nature of the system of commerce is robbery and extortion.
As with creatures in nature, the thieves & mooches & lazy & greedy people return to the natural balance, and if they don't, they are naturally selected out. Natural selection abhores thieves, moochers, the lazy & the greedy. Even the very force of people being accountable to each other in a tribal situation usually eliminates even the desire to steal or mooch or be lazy or greedy. You see it in animal societies & hunting & gathering societies.
We can see it in our own society, beginning to happen on a temporary scale at Rainbow Gatherings. There are lots and lots of moochers at Rainbow Gatherings, called "drainbows." And "So what?" is the prevailing idea. It's actually amazing how few thefts and what little violence there is at a Rainbow Gathering of 20,000 people, especially compared to a town of the same size. Towns of the same size, which have police and locks and laws and lawyers, have much more crime. Think about that. The Rainbow Gathering still miraculously works out, due to the droves and droves of hard-working, generous people, who don't give a hoot that somebody else might be "taking advantage." What is taking advantage? The philosophy is to do, expecting nothing in return. And that philosophy becomes infectious. There is a lot of rif-raf at gatherings, and a lot of true compassion that overshadows it. The idea of compassion is to have patience with thieves, mooches, the lazy, and the greedy, who are people still detoxing from being programmed by the money system.
When you have been taught all your life that nothing is valuble unless you get money for it, you will initially be lazy, because you aren't paid. You haven't yet learned the true reward of doing itself, and the reward of community with others, which makes money look ridiculous. When you have been programmed into thinking that possessing and not sharing are virtues, you tend to steal, and it takes you a while to deprogram from that. The Rainbow Gathering is a hospital, and those who caretake the hospital have a natural sense of patience with the patients, giving them all the time they need to heal. You can only be idle so long before you get sick of being idle and start wanting to contribute. It might take a while, but it happens, naturally.