The strong prey upon the weak far more in our current system than they would in a decentralized one. As for anarchist societies not having laws, your only error in that assessment is that you left a phrase incomplete:
centrally planned laws. An anarchist society's laws would much resemble English Common Law prior to the 19th century, but with the role of punitive punishment largely dropped in favor of restitution and rehabilitation. This is perfectly in line with how nations with very low recidivism rates behave, asides from the decentralized aspect.
As for the lack of rewards argument, that's not actually in line with human behavior at all.
It's actually the profit motive that doesn't sit well with human nature, as we're evolved to be social creatures who get significant emotional satisfaction from being part of a meaningful team, having greater autonomy or earning greater status among their peers. We've even found that past the point you can live without worrying about your financial well being,
more money does not translate to more happiness.
Finally, there are plenty of working societies throughout the world based off of collective good, instead of profit motive. The Kingdom of Bhutan, for example, has run its economy off of the idea of a "happiness index" instead of GDP for decades, and makes decisions calculated entirely on whether or not they will make the general population of Bhutan healthier and more satisfied with their lives. Bhutan has no homelessness, virtually no crime & is an environmentally sustainable nation with a population of 800,000. The Chiapas Autonomous Region of Mexico is an independent anarchist society, and has been so since they revolted in the wake of NAFTA. They have a population of 5 million. Every hunter-gatherer society that preceded nation-states was effectively anarchist, and voluntary conflict resolution served our ancestors perfectly well for hundreds of thousands of years before the advent of coercive states just a scant few thousand years ago.
Anarchy works, has worked, and will continue to work just fine.